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Pattern-Instanciation-On-System-Engineering-Model
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This project is a demonstrator of pattern instanciation on system engineering model (pseim), made by the MOISE project. It contains the metamodel of the pseim, graphical and textual editors, formal verification models (event-B) and examples.
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Pattern-Instanciation-On-Sy.../Event-B/pseim/mComponent.bpr

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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="inst_components∈components(Pat) ↔ components(Mdl)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c_mult_others∈components(Pat) ∖ dom(inst_components) → ℕ"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈dom(components)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="inst_components∈components(Pat) ↔ components(Mdl)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/new_c_ty/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p3,p1,p2,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20">
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)∧c∈dom(c_multiplicity(Pat))∧c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/to_unfold_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Z3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3">
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_unfold_c ∖ {c}⊆(components{Pat ↦ components(Pat)∪ran(new_c)})(Pat)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Pat∈Pattern">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components{Pat ↦ components(Pat)∪ran(new_c)})"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_free_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(c_multiplicity)">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="components{Pat ↦ components(Pat)∪ran(new_c)}∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/p_WD/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19">
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<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
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<org.eventb.core.prPred name="p39" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r6" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]">
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c">
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<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="components∈Model ↔ Component"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_clone_c∈(components∪({Mdl} × ran(new_components)))[{Inst}] ⇸ (components∪({Mdl} × ran(new_components)))[{Pat}]"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬Inst=Mdl"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/to_free_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p20,p11,p8,p1,p13,p15,p2,p3,p4,p5,p6,p7,p9,p10,p12,p14,p16,p17,p18,p19,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Mdl∈dom(container)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="(c_multiplicity(Pat))[components(Pat)]⊆{1}"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="(container(Mdl))∼;inst_components∼;container(Pat)⊆inst_components∼"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="new_components∈components(Pat) ∖ dom(inst_components) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components{Mdl ↦ components(Mdl)∪ran(new_components)})"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/to_clone_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Pat∈dom(components{Pat ↦ components(Pat)∪ran(new_c)})"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p11" org.eventb.core.predicate="c∈to_unfold_c"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="to_clone_c∪(ran(new_c) × {c})∈components(Pat)∪ran(new_c) ⇸ components(Pat)∪ran(new_c)"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="components{Pat ↦ components(Pat)∪ran(new_c)}∈Model ⇸ ℙ(Component)"/>
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Pat∈dom(components)"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(components)"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/comp/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
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<org.eventb.core.prPred name="p46" org.eventb.core.predicate="container(m)∈components(Pat)∪ran(cloned_c) ⇸ ({Pat} ⩤ components)(m)">
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="instanciation_started∈BOOL">
<org.eventb.core.prIdent name="instanciation_started" org.eventb.core.type="BOOL"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·(container{Pat ↦ container(Pat)∪(ran(cloned_c) × {c})})(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="Model"/>
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<org.eventb.core.prProof name="clone_c/to_clone_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p6"/>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="Pattern⊆Model">
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="{c} ⩤ to_clone_c∈components[{Inst}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/to_free_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p28" org.eventb.core.prHyps="p15,p19,p3,p1,p8,p27,p9,p10,p2,p11,p12,p13,p14,p16,p4,p17,p18,p5,p6,p7,p20,p21,p22,p24,p25,p26">
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Pat∈dom(components{Pat ↦ components(Pat)∪ran(cloned_c)})"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p22" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/container/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p16,p9,p1,p2,p3,p4,p5,p6,p7,p8,p10,p11,p12,p13,p14,p15,p17,p18,p19,p20,p21,p22,p23,p24">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="cloned_c∈(container(Pat))∼[{to_clone_c(c)}] ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/pc/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p16,p9,p1,p2,p3,p4,p5,p6,p7,p8,p10,p11,p12,p13,p14,p15,p17,p18,p19,p20,p21,p22,p23,p24">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(components)∧components∈Model ⇸ ℙ(Component)"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="components{Pat ↦ components(Pat) ∖ {c}}∈Model → ℙ(Component)"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/cm_ctr/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="m" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(components)"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="container(Pat)∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="(container{Pat ↦ {c} ⩤ container(Pat)})(m)∈components(Pat) ∖ {c} ⇸ (components{Pat ↦ components(Pat) ∖ {c}})(m)">
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="(container{Pat ↦ {c} ⩤ container(Pat)})(m)∈({Pat} ⩤ components)(m) ⇸ (components{Pat ↦ components(Pat) ∖ {c}})(m)">
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<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="(container{Pat ↦ {c} ⩤ container(Pat)})(m)∈(components{Pat ↦ components(Pat) ∖ {c}})(m) ⇸ (components{Pat ↦ components(Pat) ∖ {c}})(m)">
<org.eventb.core.prIdent name="m" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p41" org.eventb.core.predicate="{c} ⩤ container(Pat)∈components(Pat) ∖ {c} ⇸ ({Pat} ⩤ components)(Pat)"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="¬m=Pat">
<org.eventb.core.prIdent name="m" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="(container{Pat ↦ {c} ⩤ container(Pat)})(Pat)∈components(Pat) ∖ {c} ⇸ components(Pat) ∖ {c}"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="m=Pat">
<org.eventb.core.prIdent name="m" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="Pat"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r10" org.eventb.core.prRID="org.eventb.core.seqprover.falseHyp"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.cut"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.funOvr:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.allD"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.locEq"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/acycl/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p18,p12,p4,p14,p20,p13,p16,p2,p6,p21,p22,p15,p5,p19,p7,p11,p8,p9"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p10,p17,p3,p1,p18,p12,p4,p14,p20,p13,p16,p2,p6,p21,p22,p15,p5,p19,p7,p11,p8,p9">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c∉to_unfold_c"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·(container{Pat ↦ {c} ⩤ container(Pat)})(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/to_clone_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Z3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8">
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<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="Z3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="components{Pat ↦ components(Pat) ∖ {c}}∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_clone_c∈(components{Pat ↦ components(Pat) ∖ {c}})(Pat) ⇸ (components{Pat ↦ components(Pat) ∖ {c}})(Pat)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(components{Pat ↦ components(Pat) ∖ {c}})"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/to_free_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p28" org.eventb.core.prHyps="p16,p8,p27,p1,p26,p9,p2,p11,p12,p13,p14,p15,p3,p17,p4,p18,p5,p6,p7,p19,p20,p21,p23,p24,p25">
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<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(to_free_c ∖ {c})∪(container(Pat))∼[{c}]⊆(components{Pat ↦ components(Pat) ∖ {c}})(Pat)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∉to_unfold_c"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
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<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="⊤"/>
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<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
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<org.eventb.core.prProof name="unfold_c/comp/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prIdent name="m" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p41" org.eventb.core.predicate="c_multiplicity(m)∈({Pat} ⩤ components)(m) → ℕ">
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c∈to_unfold_c"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p54" org.eventb.core.predicate="container(m)∈({Pat} ⩤ components)(m) ⇸ ({Pat} ⩤ components)(m)">
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<org.eventb.core.prPred name="p31" org.eventb.core.predicate="({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))∈components(Pat)∪ran(new_c) ⇸ components(Pat)∪ran(new_c)"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))∈(components{Pat ↦ components(Pat)∪ran(new_c)})(m) ⇸ (components{Pat ↦ components(Pat)∪ran(new_c)})(m)">
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<org.eventb.core.prPred name="p41" org.eventb.core.predicate="({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))∈components(m) ⇸ components(m)">
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<org.eventb.core.prPred name="p33" org.eventb.core.predicate="¬m=Pat">
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
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<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
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<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prIdent name="instanciation_started" org.eventb.core.type="BOOL"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))">
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_free_c⊆(components{Pat ↦ components(Pat)∪ran(new_c)})(Pat)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components{Pat ↦ components(Pat)∪ran(new_c)})"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ">
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(c_multiplicity)">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="components{Pat ↦ components(Pat)∪ran(new_c)}∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/new_c_model/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p10,p3,p1,p9,p2,p11,p12,p13,p14,p15,p16,p17,p4,p18,p19,p5,p20,p6,p7,p8,p21,p22,p23,p24,p25">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
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<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/new_c_mult/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p10,p3,p1,p9,p2,p11,p12,p13,p14,p15,p16,p17,p4,p18,p19,p5,p20,p6,p7,p8,p21,p22,p23,p24,p25">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/new_c_container/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p10,p3,p1,p9,p2,p11,p12,p13,p14,p15,p16,p17,p4,p18,p19,p5,p20,p6,p7,p8,p21,p22,p23,p24,p25">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
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<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p9" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p10"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c0⦂Component·c0∈(to_unfold_c ∖ {c})∪ran(to_clone_c∪(ran(new_c) × {c}))⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧Pat∈dom(container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})∧container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))}∈Model ⇸ ℙ(Component × Component))∧¬(∀sc⦂ℙ(Component)·¬(c0∈sc∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c∪ran(to_clone_c)⇒(∀sc⦂ℙ(Component)·c∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component))∧{sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component)))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒¬(∀sc⦂ℙ(Component)·¬(c∈sc∧(container(Pat))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c0⦂Component·c0∈to_free_c⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧Pat∈dom(container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})∧container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))}∈Model ⇸ ℙ(Component × Component))∧(∃sc⦂ℙ(Component)·¬¬(c0∈sc∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c0⦂Component·c0∈to_free_c⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧Pat∈dom(container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})∧container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))}∈Model ⇸ ℙ(Component × Component))∧(∃sc⦂ℙ(Component)·c0∈sc∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[sc]⊆sc)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="instanciation_started∈BOOL">
<org.eventb.core.prIdent name="instanciation_started" org.eventb.core.type="BOOL"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(⋃c0⦂Component·c0∈to_free_c ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})(Pat))∼[sc]⊆sc ∣ sc})) × (⋃c0⦂Component·c0∈(to_unfold_c ∖ {c})∪ran(to_clone_c∪(ran(new_c) × {c})) ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})(Pat))∼[sc]⊆sc ∣ sc}))⊂(⋃c⦂Component·c∈to_free_c ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc})) × (⋃c⦂Component·c∈to_unfold_c∪ran(to_clone_c) ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒(∃sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="∀c0⦂Component·c0∈to_free_c⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧Pat∈dom(container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})∧container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))}∈Model ⇸ ℙ(Component × Component))∧{sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component)))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒(∃sc⦂ℙ(Component)·¬¬(c∈sc∧(container(Pat))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀c0⦂Component·c0∈to_free_c⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧Pat∈dom(container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})∧container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))}∈Model ⇸ ℙ(Component × Component))∧¬(∀sc⦂ℙ(Component)·¬(c0∈sc∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="(⋃c0⦂Component·c0∈to_free_c ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[sc]⊆sc ∣ sc})) × (⋃c0⦂Component·c0∈(to_unfold_c ∖ {c})∪ran(to_clone_c∪(ran(new_c) × {c})) ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[sc]⊆sc ∣ sc}))⊂(⋃c⦂Component·c∈to_free_c ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc})) × (⋃c⦂Component·c∈to_unfold_c∪ran(to_clone_c) ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒{sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component)))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c∪ran(to_clone_c)⇒(∀sc⦂ℙ(Component)·c∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component))∧¬(∀sc⦂ℙ(Component)·¬(c∈sc∧(container(Pat))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀c0⦂Component·c0∈(to_unfold_c ∖ {c})∪ran(to_clone_c∪(ran(new_c) × {c}))⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧Pat∈dom(container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})∧container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))}∈Model ⇸ ℙ(Component × Component))∧{sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ ({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat))})(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component)))"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/VAR" org.eventb.core.confidence="0" org.eventb.core.prFresh="sc,s,i,c0" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="rewrite ⊂ in goal" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p1">
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="generalized MP" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="p4" org.eventb.core.prInfHyps="p3"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p1" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p9">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬(∀sc·¬(sc⊆ℕ × components[{Pat}]∧(∀c·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c0·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)∧(∀c0·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i,c,s·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p10" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p11"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p11"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬(∀sc·¬(sc⊆ℕ × components[{Pat}]∧(∀c·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i,c,s·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p12" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p13"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p13"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬¬([[0]]⊆ℕ × components[{Pat}]∧(∀c·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆[[1]])∧(∀c0·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆[[1]])∧(∀c0·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆[[1]])∧(∀i,c,s·i ↦ c∈[[3]]∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆[[3]]))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p11" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p14"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p14"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬¬([[0]]⊆ℕ × components[{Pat}]∧(∀c·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆[[1]])∧(∀c·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆[[1]])∧(∀c·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆[[1]])∧(∀i,c,s·i ↦ c∈[[3]]∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆[[3]]))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p13" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p15"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p15"/>
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p16"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p17"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p18" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p19"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p19" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p20"/>
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∃ hyp (∃sc·sc⊆ℕ × components[{Pat}]∧(∀c·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c0·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)∧(∀c0·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i,c,s·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p14" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p21,p22,p23,p24,p25">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prHypAction>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p21,p22,p23,p24,p25"/>
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∃ hyp (∃sc·sc⊆ℕ × components[{Pat}]∧(∀c·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i,c,s·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p15" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p26,p27,p28,p29,p30">
<org.eventb.core.prIdent name="sc0" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prHypAction>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p26,p27,p28,p29,p30"/>
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p31">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prRule name="r7" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⇒ goal" org.eventb.core.prGoal="p31" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p33" org.eventb.core.prHyps="p21,p32,p23,p24,p25">
<org.eventb.core.prRule name="r8" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p33" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p24">
<org.eventb.core.prRule name="r9" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="hyp" org.eventb.core.prGoal="p24" org.eventb.core.prHyps="p24"/>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p32">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p34">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p36" org.eventb.core.prHyps="p35">
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<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p39">
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<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prAnte name="*" org.eventb.core.prGoal="p43">
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<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prPred name="p52" org.eventb.core.predicate="¬{sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}={sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="c0∈ran(to_clone_c)">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc0">
<org.eventb.core.prIdent name="sc0" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="∀sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]⇒(∀c⦂Component·c∈to_unfold_c⇒c∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ)∧((∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)⇒(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒finite(to_clone_c∼[{c0}] ∖ {c}))∧((∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)⇒to_clone_c∈Component ⇸ Component∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒finite((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]))∧((∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)⇒(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒s∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ))))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∃sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="c0∈to_unfold_c">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="c0∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c0) × {c0}⊆sc">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]⇒(∀c⦂Component·c∈to_unfold_c⇒c∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ)∧((∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)⇒(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒finite(to_clone_c∼[{c0}] ∖ {c}))∧((∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)⇒c∈dom(to_clone_c)∧to_clone_c∈Component ⇸ Component∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒finite((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]))∧((∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)⇒(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒s∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ))))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="i ↦ c0∈sc">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc0">
<org.eventb.core.prIdent name="sc0" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)⇒sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∃sc⦂ℙ(ℤ×Component)·¬¬(sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc0∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc0">
<org.eventb.core.prIdent name="sc0" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]⇒(∀c⦂Component·c∈to_unfold_c⇒c∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ)∧((∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)⇒(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒finite(({c} ⩤ to_clone_c)∼[{c0}]))∧((∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(({c} ⩤ to_clone_c)∼[{c0}]) × {c0}⊆sc)⇒(∀c0⦂Component·c∈dom(to_clone_c)∧to_clone_c∈Component ⇸ Component∧(c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒finite((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}])))∧((∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)⇒(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒s∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ))))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="¬(∀sc⦂ℙ(ℤ×Component)·¬(sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="{sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(({c} ⩤ to_clone_c)∼[{c0}]) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}⊆{sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="{sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(({c} ⩤ to_clone_c)∼[{c0}]) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}⊂{sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∃sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc0">
<org.eventb.core.prIdent name="sc0" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="¬(∀sc⦂ℙ(ℤ×Component)·¬(sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="∀sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]⇒(∀c⦂Component·c∈to_unfold_c⇒c∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ)∧((∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)⇒(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒finite(({c} ⩤ to_clone_c)∼[{c0}]))∧((∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(({c} ⩤ to_clone_c)∼[{c0}]) × {c0}⊆sc)⇒(∀c0⦂Component·c∈dom(to_clone_c)∧to_clone_c∈Component ⇸ Component∧(c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒finite((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}])))∧((∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)⇒(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒s∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ))))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∃sc⦂ℙ(ℤ×Component)·¬¬(sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="sc⊆ℕ × components[{Pat}]">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="1 ‥ i∗c_multiplicity(s) × {s}⊆sc">
<org.eventb.core.prIdent name="i" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="∀sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]⇒(∀c⦂Component·c∈to_unfold_c⇒c∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ)∧((∀c⦂Component·c∈to_unfold_c⇒1 ‥ c_multiplicity(c) × {c}⊆sc)⇒(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒finite(({c} ⩤ to_clone_c)∼[{c0}]))∧((∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(({c} ⩤ to_clone_c)∼[{c0}]) × {c0}⊆sc)⇒(∀c0⦂Component·⊤∧to_clone_c∈Component ⇸ Component∧(c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒finite((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}])))∧((∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)⇒(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒s∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ))))"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="¬{sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(({c} ⩤ to_clone_c)∼[{c0}]) × {c0}⊆sc)∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}={sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc) ∣ sc}"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="1 ‥ 1+c_multiplicity(c0) × {c0}⊆sc">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="s ↦ c0∈container">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)∧(∀c⦂Component·c∈ran(to_clone_c)⇒1 ‥ card(to_clone_c∼[{c}]) × {c}⊆sc)∧(∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c}]) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆sc)">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]⇒(∀c⦂Component·c∈to_unfold_c⇒c∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ)∧((∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc)⇒(∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒finite(to_clone_c∼[{c0}] ∖ {c}))∧((∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc)⇒⊤∧to_clone_c∈Component ⇸ Component∧(∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒finite((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]))∧((∀c0⦂Component·c0∈dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⇒1 ‥ card((to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))[{c0}]) × {c0}⊆sc)⇒(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒s∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ))))"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="1 ‥ card(to_clone_c∼[{c0}]) × {c0}⊆sc">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c⇒1 ‥ 1+c_multiplicity(c) × {c}⊆sc">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="c0∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{c0}]) × {c0}⊆sc">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="c0∈dom(to_unfold_c_in)">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.sir"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.core.seqprover.hyp"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/f/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p2,p4,p5,p6,p7,p8,p22,p9,p10,p11,p12,p13,p14,p15,p17,p18,p19,p20,p21"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p16,p3,p1,p2,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p17,p18,p19,p20,p21">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c∉to_unfold_c"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/VAR" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p15">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p1" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p2"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6,p7,p8"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p9" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p10"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p11" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p12"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p13" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p14"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬(∀sc·¬([[1]]∈sc∧(container(Pat))∼[sc] ∖ {c}⊆sc))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p8" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p16"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p16"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬(∀sc·¬([[1]]∈sc∧(container(Pat))∼[sc]⊆sc))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p12" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p17"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p17"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬¬([[1]]∈[[0]]∧(container(Pat))∼[[[0]]] ∖ {c}⊆[[0]])" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p16" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p18"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p18"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬¬([[1]]∈[[0]]∧(container(Pat))∼[[[0]]]⊆[[0]])" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p17" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p19"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p19"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p20"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p21"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="1.1.1"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="1.1.1.1"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="1.1"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="1.1.1"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c0⦂Component·c0∈(to_free_c ∖ {c})∪(container(Pat))∼[{c}]⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container{Pat ↦ {c} ⩤ container(Pat)})∧container{Pat ↦ {c} ⩤ container(Pat)}∈Model ⇸ ℙ(Component × Component))∧(∃sc⦂ℙ(Component)·c0∈sc∧(container(Pat))∼[sc] ∖ {c}⊆sc)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒¬(∀sc⦂ℙ(Component)·¬(c∈sc∧(container(Pat))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c0⦂Component·c0∈to_unfold_c∪ran(to_clone_c)⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container{Pat ↦ {c} ⩤ container(Pat)})∧container{Pat ↦ {c} ⩤ container(Pat)}∈Model ⇸ ℙ(Component × Component))∧¬(∀sc⦂ℙ(Component)·¬(c0∈sc∧(container(Pat))∼[sc] ∖ {c}⊆sc))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c∉to_unfold_c"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒(∃sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c0⦂Component·c0∈(to_free_c ∖ {c})∪(container(Pat))∼[{c}]⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container{Pat ↦ {c} ⩤ container(Pat)})∧container{Pat ↦ {c} ⩤ container(Pat)}∈Model ⇸ ℙ(Component × Component))∧¬(∀sc⦂ℙ(Component)·¬(c0∈sc∧(container(Pat))∼[sc] ∖ {c}⊆sc))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒(∃sc⦂ℙ(Component)·¬¬(c∈sc∧(container(Pat))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬c∈to_unfold_c"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀c0⦂Component·Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧(c0∈(to_free_c ∖ {c})∪(container(Pat))∼[{c}]⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container{Pat ↦ {c} ⩤ container(Pat)})∧container{Pat ↦ {c} ⩤ container(Pat)}∈Model ⇸ ℙ(Component × Component))∧{sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ {c} ⩤ container(Pat)})(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component))))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Mdl∈Model">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(⋃c0⦂Component·c0∈(to_free_c ∖ {c})∪(container(Pat))∼[{c}] ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ {c} ⩤ container(Pat)})(Pat))∼[sc]⊆sc ∣ sc})) × (⋃c0⦂Component·c0∈to_unfold_c∪ran(to_clone_c) ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ {c} ⩤ container(Pat)})(Pat))∼[sc]⊆sc ∣ sc}))⊂(⋃c⦂Component·c∈to_free_c ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc})) × (⋃c⦂Component·c∈to_unfold_c∪ran(to_clone_c) ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀c⦂Component·c∈to_free_c⇒{sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component)))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c∪ran(to_clone_c)⇒{sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component)))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="(⋃c0⦂Component·c0∈(to_free_c ∖ {c})∪(container(Pat))∼[{c}] ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧(container(Pat))∼[sc] ∖ {c}⊆sc ∣ sc})) × (⋃c0⦂Component·c0∈to_unfold_c∪ran(to_clone_c) ∣ {c0} × inter({sc⦂ℙ(Component)·c0∈sc∧(container(Pat))∼[sc] ∖ {c}⊆sc ∣ sc}))⊂(⋃c⦂Component·c∈to_free_c ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc})) × (⋃c⦂Component·c∈to_unfold_c∪ran(to_clone_c) ∣ {c} × inter({sc⦂ℙ(Component)·c∈sc∧(container(Pat))∼[sc]⊆sc ∣ sc}))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c0⦂Component·c0∈(to_free_c ∖ {c})∪(container(Pat))∼[{c}]⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container{Pat ↦ {c} ⩤ container(Pat)})∧container{Pat ↦ {c} ⩤ container(Pat)}∈Model ⇸ ℙ(Component × Component))∧(∃sc⦂ℙ(Component)·¬¬(c0∈sc∧(container(Pat))∼[sc] ∖ {c}⊆sc))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c0⦂Component·c0∈to_unfold_c∪ran(to_clone_c)⇒(∀sc⦂ℙ(Component)·c0∈sc⇒Pat∈dom(container{Pat ↦ {c} ⩤ container(Pat)})∧container{Pat ↦ {c} ⩤ container(Pat)}∈Model ⇸ ℙ(Component × Component))∧{sc⦂ℙ(Component)·c0∈sc∧((container{Pat ↦ {c} ⩤ container(Pat)})(Pat))∼[sc]⊆sc ∣ sc}≠(∅ ⦂ ℙ(ℙ(Component)))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c∪ran(to_clone_c)⇒¬(∀sc⦂ℙ(Component)·¬(c∈sc∧(container(Pat))∼[sc]⊆sc))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/to_unfold_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p10" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p11"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p12" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p13"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p14" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p15"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p16" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p17"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p18" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p19"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p20" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p21"/>
<org.eventb.core.prHypAction name="REWRITE6" org.eventb.core.prHidden="p22" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p23"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p24"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p25"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="PP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p9,p7,p8,p5,p2,p1,p6,p4,p3">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_unfold_c⊆(components∪({Mdl} × ran(new_components)))[{Pat}]"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="containers[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="ran(new_components)∩ran(containers)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="ran(new_components)∩ran(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="dom(inst_components) ◁ containers;inst_components⊆inst_components;containers"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/to_unfold_c/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p28">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p23" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p27"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p8,p27,p9,p10,p2,p11,p12,p13,p14,p29,p15,p16,p4,p17,p18,p5,p6,p7,p20,p21,p22,p25,p26"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p28" org.eventb.core.prHyps="p24,p19,p3,p1,p8,p27,p9,p10,p2,p11,p12,p13,p14,p15,p16,p4,p17,p18,p5,p6,p7,p20,p21,p22,p25,p26">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(to_unfold_c ∖ {c})∪ran(cloned_c)⊆(components{Pat ↦ components(Pat)∪ran(cloned_c)})(Pat)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="cloned_c∈(container(Pat))∼[{to_clone_c(c)}] ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Pat∈dom(components{Pat ↦ components(Pat)∪ran(cloned_c)})"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_multiplicity{Pat ↦ ae}∈Pattern → (Component ⇸ ℕ)">
<org.eventb.core.prIdent name="ae" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="c_multiplicity{Pat ↦ c_multiplicity(Pat)∪(cloned_c∼;c_multiplicity(Pat))}∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prExpr name="e1" org.eventb.core.expression="Pat"/>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="c_multiplicity(Pat)∪(cloned_c∼;c_multiplicity(Pat))"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.allD"/>
<org.eventb.core.prReas name="r10" org.eventb.core.prRID="org.eventb.core.seqprover.he:1"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.hyp"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allmpD:0"/>
<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.core.seqprover.ae"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r11" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.cut"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/mult/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p16,p9,p1,p2,p3,p4,p5,p6,p7,p8,p10,p11,p12,p13,p14,p15,p17,p18,p19,p20,p21,p22,p23,p24">
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<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="cloned_c∈(container(Pat))∼[{to_clone_c(c)}] ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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<org.eventb.core.prProof name="instanciate_pattern/cm/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p6" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p7"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="⊤∧⊤"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Inst≠Mdl">
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<org.eventb.core.prIdent name="c_mult_others" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ1)">
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)">
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_free_c⊆components(Pat)">
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_index∈Component ⇸ ℤ"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c∈dom(c_index)∧c_index∈Component ⇸ ℤ∧inst2pat_c∈Component ⇸ Component∧inst2pat_c(c)∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="inst2pat_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈dom(c_index)∧c_index∈Component ⇸ ℤ∧inst2pat_c∈Component ⇸ Component∧inst2pat_c(c)∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="c∈dom(inst2pat_c)⇒c∈dom(c_index)∧c_index∈Component ⇸ ℤ∧inst2pat_c∈Component ⇸ Component∧inst2pat_c(c)∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="inst2pat_c(c)∈components[{Pat}]">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c∈dom(inst2pat_c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="dom(inst2pat_c)"/>
<org.eventb.core.prExpr name="e1" org.eventb.core.expression="components[{Pat}]"/>
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<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.funImgGoal"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/to_clone_c_mult/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component">
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p9" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p10"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p11" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p12"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂Component·c∈dom(∅ ⦂ ℙ(Component×Component))⇒(∅ ⦂ ℙ(Component×ℤ))(c)∈1 ‥ c_mult((∅ ⦂ ℙ(Component×Component))(c))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="⊤"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
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</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)">
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_free_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
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<org.eventb.core.prPred name="p33" org.eventb.core.predicate="finite(new_components[components[{Inst}] ∖ dom(inst_components)])"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_free_c⊆components(Pat)">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈Pattern">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))">
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)">
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(∅ ⦂ ℙ(Component×Component))∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Pat∈dom(components)">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈dom(components)">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/to_free_to_clone_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p14,p10,p3,p1,p21,p4,p2,p6,p23,p18,p8,p16,p9,p13,p24,p25,p7,p11,p22,p15,p17,p20,p19,p5,p12">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_clone_c∪(ran(new_c) × {c}))∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/to_free_to_clone_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p7,p16,p9,p1,p18,p12,p4,p14,p20,p13,p17,p10,p3,p6,p22,p23,p15,p5,p19,p8,p11,p24,p21,p2">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(({c} ⩤ to_clone_c)∪cloned_c∼)∩(to_free_c∪{c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="cloned_c∈(container(Pat))∼[{to_clone_c(c)}] ↣ Component ∖ union(ran(components))"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p11">
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<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p9"/>
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<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="0.1.1"/>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="c∈ran(container(Pat))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="dom(to_clone_c)∩((to_free_c ∖ {c})∪{(container(Pat))∼(c)})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="c∈dom((container(Pat))∼)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧c∈dom((container(Pat))∼)∧(container(Pat))∼∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_clone_c)∩((to_free_c ∖ {c})∪(container(Pat))∼[{c}])=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="instanciation_started∈BOOL">
<org.eventb.core.prIdent name="instanciation_started" org.eventb.core.type="BOOL"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="(container(Pat))∼∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.funSingletonImg"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.hyp"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/to_free_dom_to_clone_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="PP (trivial)" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_free_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈Pattern">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(∅ ⦂ ℙ(Component×Component))∩(components(Pat) ∖ dom(container(Pat)))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈dom(components)">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/to_free_dom_to_clone_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p14,p10,p3,p1,p9,p2,p11,p12,p13,p15,p16,p17,p4,p18,p19,p5,p20,p6,p7,p8,p21,p22,p23,p24,p25">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_clone_c∪(ran(new_c) × {c}))∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/to_free_dom_to_clone_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p8,p25,p10,p11,p12,p13,p14,p15,p17,p18,p19,p20,p21,p22,p23,p24"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p7,p16,p9,p1,p2,p3,p4,p5,p6,p8,p10,p11,p12,p13,p14,p15,p17,p18,p19,p20,p21,p22,p23,p24">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="cloned_c∈(container(Pat))∼[{to_clone_c(c)}] ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(({c} ⩤ to_clone_c)∪cloned_c∼)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/to_free_dom_to_clone_disjoint/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p16" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p20"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p21"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∪ / ∩ distribution in goal" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p22">
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="fun. singleton img. in goal" org.eventb.core.prGoal="p22" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p23">
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p23" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p17">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="hyp" org.eventb.core.prGoal="p17" org.eventb.core.prHyps="p17"/>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p15">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="hyp" org.eventb.core.prGoal="p15" org.eventb.core.prHyps="p15"/>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p24">
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p24" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p25"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="*" org.eventb.core.prGoal="p26"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p27">
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p27" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p28">
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p28" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p29">
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p20,p1,p2,p3,p4,p6,p7,p8,p9,p10,p11,p12,p14,p15,p18,p19,p17"/>
<org.eventb.core.prRule name="r7" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p29" org.eventb.core.prHyps="p20,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p18,p19,p17">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p30"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="0.1.1"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="0.1"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_clone_c)∩((to_free_c ∖ {c})∪(container(Pat))∼[{c}])=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="(dom(to_clone_c)∩(to_free_c ∖ {c}))∪(dom(to_clone_c)∩{(container(Pat))∼(c)})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c∈dom((container(Pat))∼)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="¬(container(Pat))∼(c)∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c⊆{c}"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="(container(Pat))∼∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c⊆{c}∧¬(container(Pat))∼(c)∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="c∈ran(container(Pat))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="(dom(to_clone_c)∩(to_free_c ∖ {c}))∪(dom(to_clone_c)∩(container(Pat))∼[{c}])=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)∧c∈dom((container(Pat))∼)∧(container(Pat))∼∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.funSingletonImg"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.hyp"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.unionInterDistRewrites"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/to_unfold_dom_to_clone_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="PP (trivial)" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="instanciation_started∈BOOL">
<org.eventb.core.prIdent name="instanciation_started" org.eventb.core.type="BOOL"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_free_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈Pattern">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(∅ ⦂ ℙ(Component×Component))∩(components(Pat) ∖ dom(container(Pat)))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Mdl∈dom(components)">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/to_unfold_dom_to_clone_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p22,p4,p2,p6,p24,p18,p8,p16,p9,p13,p25,p26,p7,p11,p23,p14,p17,p15,p20,p19,p5,p12"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p21,p10,p3,p1,p22,p4,p2,p6,p24,p18,p8,p16,p9,p13,p25,p26,p7,p11,p23,p14,p17,p15,p20,p19,p5,p12">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_clone_c∪(ran(new_c) × {c}))∩(to_unfold_c ∖ {c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="dom(to_clone_c)∩to_unfold_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/to_unfold_dom_to_clone_disjoint/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prHyps="">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p0" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p1"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p2"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p3"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="instanciation_started∈BOOL">
<org.eventb.core.prIdent name="instanciation_started" org.eventb.core.type="BOOL"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="end_instanciation/p_WD/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p2,p20,p14,p4,p17,p22,p15,p19,p12,p3,p7,p23,p24,p18,p6,p21,p8,p13,p5,p9"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p10,p1,p11,p16,p2,p20,p14,p4,p17,p22,p15,p19,p12,p3,p7,p23,p24,p18,p6,p21,p8,p13,p5,p9">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="instanciation_started" org.eventb.core.type="BOOL"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="instanciation_started=TRUE"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_unfold_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)∧Pat∈dom(components)∧components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_clone_c=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="instanciation_started∈BOOL"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/to_free_to_unfold_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="PP (trivial)" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(components(Pat) ∖ dom(container(Pat)))∩(∅ ⦂ ℙ(Component))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_free_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈Pattern">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈dom(components)">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_c/to_free_to_unfold_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p22,p4,p2,p6,p24,p19,p8,p17,p9,p13,p25,p26,p7,p11,p23,p14,p18,p15,p21,p20,p5,p12"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p16,p10,p3,p1,p22,p4,p2,p6,p24,p19,p8,p17,p9,p13,p25,p26,p7,p11,p23,p14,p18,p15,p21,p20,p5,p12">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(to_unfold_c ∖ {c})∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/to_free_to_unfold_disjoint/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p19,p4,p2,p5,p21,p17,p7,p15,p9,p11,p23,p24,p6,p10,p20,p12,p16,p13,p25,p22,p8"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p14,p18,p3,p1,p19,p4,p2,p5,p21,p17,p7,p15,p9,p11,p23,p24,p6,p10,p20,p12,p16,p13,p25,p22,p8">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="cloned_c∈(container(Pat))∼[{to_clone_c(c)}] ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="((to_unfold_c ∖ {c})∪ran(cloned_c))∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_clone_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p22" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/to_free_to_unfold_disjoint/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prHyps="">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p0" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p1"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p4"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬c∈to_unfold_c">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c∉to_unfold_c">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
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</org.eventb.core.prProof>
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<org.eventb.core.lang name="L"/>
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)">
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="components(Pat) ∖ dom(container(Pat))⊆components(Pat)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈dom(components)">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/cm/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p2,p18,p3,p1,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p19,p20,p21,p22,p23">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="c_multiplicity{Pat ↦ {c} ⩤ c_multiplicity(Pat)}∈Pattern → (Component ⇸ ℕ)"/>
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<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="free_c/to_clone_c_mult/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_free_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/to_free_c/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.finiteSet:0"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/comp_disj/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p2,p28,p10,p30,p19,p31,p7,p4,p20,p6,p18,p12,p25,p21,p8,p29,p14,p1,p22,p16,p15,p3,p5,p26,p11,p27"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p9,p17,p13,p23,p24,p2,p28,p10,p30,p19,p31,p7,p4,p20,p6,p18,p12,p25,p21,p8,p29,p14,p1,p22,p16,p15,p3,p5,p26,p11,p27">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_mult_others" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="pat_roots" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="inst_components∼∈components[{Mdl}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="to_clone_c⊆inst2pat_c"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="inst_components∈components[{Pat}] ↔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="({Inst} ⩤ components)∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_mult_others∈components[{Pat}] ∖ dom(inst_components) → ℕ"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="pat_roots=components[{Pat}] ∖ dom(container)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="components∈Model ↔ Component"/>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_mult_others" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
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</org.eventb.core.prAnte>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="¬Inst=Mdl">
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(components)∧components∈Model ⇸ ℙ(Component)∧Pat∈dom(container)∧container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Inst≠Mdl">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pat∈dom(container)"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_mult_others" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_clone_c⊆inst2pat_c">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p17" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)">
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<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]">
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prPred name="p33" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
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<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
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<org.eventb.core.prString name=".pos" org.eventb.core.prSValue=""/>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c0⦂Component·c0∈(components∪({Inst} × ran(new_c)))[{Pat}]⇒¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒dom(c_indexes(i))=(containers∪(id ⦂ ℙ(Component×Component)))[{inst2pat_c(i)}]"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="finite(ran(new_c))"/>
<org.eventb.core.prPred name="p119" org.eventb.core.predicate="∀i⦂Component·i∈ran(new_c)⇒i∈ran(new_c)∧new_c∼∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p110" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="M=max(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p121" org.eventb.core.predicate="c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p61" org.eventb.core.predicate="∀c0⦂Component·c0∈(components∪({Inst} × ran(new_c)))[{Pat}]⇒(∀s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}]⇒ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x))∧c0∈dom(todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ (to_unfold_c_in[{s}]∪ran(new_c)) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))})∧todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ (to_unfold_c_in[{s}]∪ran(new_c)) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))}∈Component ⇸ ℙ(Component × ℙ(Component × ℤ))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(Component×ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p84" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p133" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)"/>
<org.eventb.core.prPred name="p103" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ 0)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p137" org.eventb.core.predicate="¬new_c⊆(∅ ⦂ ℙ(ℤ×Component))"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="∀c0⦂Component·c0∈(components∪({Inst} × ran(new_c)))[{Pat}]⇒ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p98" org.eventb.core.predicate="max(ran(c_multiplicity))=0"/>
<org.eventb.core.prPred name="p107" org.eventb.core.predicate="todo∈ℙ({∅ ⦂ ℙ(Component×ℤ)})">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="∀c0⦂Component·c0∈(components∪({Inst} × ran(new_c)))[{Pat}]⇒(∀s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}]⇒¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x))∧c0∈dom(todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ (to_unfold_c_in[{s}]∪ran(new_c)) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))})∧todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ (to_unfold_c_in[{s}]∪ran(new_c)) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))}∈Component ⇸ ℙ(Component × ℙ(Component × ℤ))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(Component×ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p132" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)"/>
<org.eventb.core.prPred name="p96" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x)"/>
<org.eventb.core.prPred name="p142" org.eventb.core.predicate="x ↦ x0∈new_c">
<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p92" org.eventb.core.predicate="(∅ ⦂ ℙ(ℙ(Component×ℤ)))⊆todo∩{k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p27" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p89" org.eventb.core.predicate="todo∩{k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}=(∅ ⦂ ℙ(ℙ(Component×ℤ)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p28" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒c_indexes(i)=inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index)"/>
<org.eventb.core.prPred name="p97" org.eventb.core.predicate="¬⊥∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x)"/>
<org.eventb.core.prPred name="p111" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p91" org.eventb.core.predicate="todo∩{k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}⊆(∅ ⦂ ℙ(ℙ(Component×ℤ)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p124" org.eventb.core.predicate="c_multiplicity(c)∈ran(c_multiplicity)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p117" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p130" org.eventb.core.predicate="(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ c_indexes[dom(inst2pat_c)]⊆(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]"/>
<org.eventb.core.prPred name="p131" org.eventb.core.predicate="∀x⦂ℙ(Component×ℤ)·x∈(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ c_indexes[dom(inst2pat_c)]⇒x∈(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p87" org.eventb.core.predicate="todo⊆todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p80" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p120" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p75" org.eventb.core.predicate="⊥"/>
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<org.eventb.core.prPred name="p116" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p81" org.eventb.core.predicate="todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ {c ↦ k}}=todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p40" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p122" org.eventb.core.predicate="c∈dom(c_multiplicity)∧c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p139" org.eventb.core.predicate="¬(∀x⦂ℤ,x0⦂Component·¬x ↦ x0∈new_c)"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p144" org.eventb.core.predicate="{c ↦ x}∈(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]">
<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p49" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p136" org.eventb.core.predicate="¬(new_c⊆(∅ ⦂ ℙ(ℤ×Component))∧(∅ ⦂ ℙ(ℤ×Component))⊆new_c)"/>
<org.eventb.core.prPred name="p108" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → (∅ ⦂ ℙ(ℤ))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p141" org.eventb.core.predicate="∃x⦂ℤ,x0⦂Component·x ↦ x0∈new_c"/>
<org.eventb.core.prPred name="p123" org.eventb.core.predicate="⊤∧⊤"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
<org.eventb.core.prIdent name="b" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p99" org.eventb.core.predicate="M=0"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p102" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ 0)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p74" org.eventb.core.predicate="(P ⇸ 1 ‥ M) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]=(P ⇸ 1 ‥ M) ∖ c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p106" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ {∅ ⦂ ℙ(Component×ℤ)}"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p126" org.eventb.core.predicate="(P ⇸ 1 ‥ M) ∖ c_indexes[dom(inst2pat_c)]⊆(P ⇸ 1 ‥ M) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p77" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="(P ⇸ 1 ‥ M) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]⊆(P ⇸ 1 ‥ M) ∖ c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p115" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p88" org.eventb.core.predicate="todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}⊆todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p104" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ 0∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p78" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo">
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<org.eventb.core.prPred name="p112" org.eventb.core.predicate="∀c⦂Component,s⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧s ↦ c∈containers∪(id ⦂ ℙ(Component×Component))∧m∈ran(c_indexes)⇒s∉dom(m)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p85" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(P ⇸ 1 ‥ M) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]⊂(P ⇸ 1 ‥ M) ∖ c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p90" org.eventb.core.predicate="todo⊆todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p94" org.eventb.core.predicate="∀x⦂ℙ(Component×ℤ)·¬x∈todo∩{k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}">
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p95" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p143" org.eventb.core.predicate="{c ↦ x}∈(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ c_indexes[dom(inst2pat_c)]">
<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p82" org.eventb.core.predicate="todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}=todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p105" org.eventb.core.predicate="∀x⦂ℙ(Component×ℤ)·¬x∈todo∩{k⦂ℤ·k∈1 ‥ 0 ∣ {c ↦ k}}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p113" org.eventb.core.predicate="∀c⦂Component,s⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧s ↦ c∈containers∪(id ⦂ ℙ(Component×Component))∧m∈ran(c_indexes)⇒¬s∈dom(m)"/>
<org.eventb.core.prPred name="p128" org.eventb.core.predicate="(P ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ c_indexes[dom(inst2pat_c)]⊆(P ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="∀m⦂ℙ(Component×ℤ),p⦂Component·m∈todo∧p∈dom(m)⇒containers[{p}]⊆dom(m)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x)"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p118" org.eventb.core.predicate="∀i⦂Component·i∈ran(new_c)⇒i∈dom(new_c∼)∧new_c∼∈Component ⇸ ℤ"/>
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<org.eventb.core.prPred name="p30" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p79" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i)∪{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p129" org.eventb.core.predicate="(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]⊆(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity))) ∖ c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p101" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ 0⇒c_indexes(i)∪{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p68" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p38" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
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<org.eventb.core.prPred name="p134" org.eventb.core.predicate="ran(new_c)≠(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="∀c0⦂Component·c0∈(components∪({Inst} × ran(new_c)))[{Pat}]⇒(∀s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}]⇒¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x))∧c0∈dom(todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ ran(new_c) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))})∧todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ ran(new_c) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))}∈Component ⇸ ℙ(Component × ℙ(Component × ℤ))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(Component×ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p70" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i)∪{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p93" org.eventb.core.predicate="∀x⦂ℙ(Component×ℤ)·x∈todo∩{k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ {c ↦ k}}⇒x∈(∅ ⦂ ℙ(ℙ(Component×ℤ)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p86" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="∀c0⦂Component·c0∈(components∪({Inst} × ran(new_c)))[{Pat}]⇒(∀s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}]⇒ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x))∧c0∈dom(todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ ran(new_c) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))})∧todo{c ↦ (∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))}{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ ran(new_c) × (containers∼[{s}] → 0 ‥ max(ran(c_multiplicity)))}∈Component ⇸ ℙ(Component × ℙ(Component × ℤ))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(Component×ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p109" org.eventb.core.predicate="todo⊆{∅ ⦂ ℙ(Component×ℤ)}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p56" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x)"/>
<org.eventb.core.prPred name="p100" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ 0⇒{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p76" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
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<org.eventb.core.prPred name="p46" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p73" org.eventb.core.predicate="¬(P ⇸ 1 ‥ M) ∖ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ {c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]=(P ⇸ 1 ‥ M) ∖ c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p140" org.eventb.core.predicate="∃x⦂ℤ,x0⦂Component·¬¬x ↦ x0∈new_c"/>
<org.eventb.core.prPred name="p83" org.eventb.core.predicate="finite(components[{Pat}])"/>
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<org.eventb.core.prPred name="p50" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p125" org.eventb.core.predicate="¬max(ran(c_multiplicity))=0"/>
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<org.eventb.core.prReas name="r12" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r16" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r17" org.eventb.core.prRID="org.eventb.core.seqprover.cut"/>
<org.eventb.core.prReas name="r13" org.eventb.core.prRID="org.eventb.core.seqprover.hyp"/>
<org.eventb.core.prReas name="r18" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r19" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.setEqlRewrites"/>
<org.eventb.core.prReas name="r11" org.eventb.core.prRID="org.eventb.core.seqprover.doCase"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r14" org.eventb.core.prRID="org.eventb.core.seqprover.rmL1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r15" org.eventb.core.prRID="org.eventb.core.seqprover.allmpD:0"/>
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<org.eventb.core.prProof name="unfold_node_c/VAR" org.eventb.core.confidence="1000" org.eventb.core.prFresh="b,ae,x,x0" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49,p50,p51,p52,p53" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
<org.eventb.core.lang name="L"/>
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<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p54" org.eventb.core.prHyps="p45">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p44" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p56"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p45" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p57"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p58"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p59"/>
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="rewrite ⊂ in goal" org.eventb.core.prGoal="p54" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p60">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p60" org.eventb.core.prHyps="p57,p28,p25,p3,p5">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}[dom(inst2pat_c)]⊆c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p118" org.eventb.core.predicate="1≤x">
<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p76" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="c_indexes[dom(ran(new_c) × {c})]∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}[dom(ran(new_c) × {c})]⊆c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})[dom(inst2pat_c)∪dom(ran(new_c) × {c})]⊆c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p77" org.eventb.core.predicate="∀m⦂ℙ(Component×ℤ),p⦂Component·m∈todo∧p∈dom(m)⇒containers[{p}]⊆dom(m)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p78" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p112" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}[dom(ran(new_c) × {c})]⊆c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})[dom(inst2pat_c∪(ran(new_c) × {c}))]⊆c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p80" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p110" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in∧x∈1 ‥ M">
<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p94" org.eventb.core.predicate="∀x⦂ℙ(Component×ℤ)·x∈{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}[ran(new_c)]⇒x∈c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p106" org.eventb.core.predicate="c_indexes(dest){c ↦ x}∈{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}[ran(new_c)]">
<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p81" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ M)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p95" org.eventb.core.predicate="ran(new_c)≠(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p92" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p73" org.eventb.core.predicate="c_indexes[dom(ran(new_c) × {c})]⊆c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p82" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p103" org.eventb.core.predicate="∀i⦂Component·i∈ran(new_c)⇒⊥∧c_indexes∈Component ⇸ ℙ(Component × ℤ)∧i∈ran(new_c)∧new_c∼∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p84" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p69" org.eventb.core.predicate="c_indexes[dom(inst2pat_c)]∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}[dom(inst2pat_c)]⊆c_indexes[dom(inst2pat_c)]"/>
<org.eventb.core.prPred name="p102" org.eventb.core.predicate="dest∈dom(c_indexes)"/>
<org.eventb.core.prPred name="p89" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p96" org.eventb.core.predicate="¬new_c=(∅ ⦂ ℙ(ℤ×Component))"/>
<org.eventb.core.prPred name="p115" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∉ran(c_indexes)⇒m∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
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<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p128" org.eventb.core.predicate="ae⊆P ⇸ 1 ‥ M">
<org.eventb.core.prIdent name="ae" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
</org.eventb.core.prExpr>
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<org.eventb.core.prExpr name="e3" org.eventb.core.expression="c_indexes(dest){c ↦ x}">
<org.eventb.core.prIdent name="x" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prExpr name="e1" org.eventb.core.expression="dest"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.sir"/>
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<org.eventb.core.prReas name="r20" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r10" org.eventb.core.prRID="org.eventb.core.seqprover.relImgUnionRightRewrites"/>
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<org.eventb.core.prReas name="r11" org.eventb.core.prRID="org.eventb.core.seqprover.relImgUnionLeftRewrites"/>
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<org.eventb.core.prProof name="unfold_root_c/inst_2_pat_c/INV"/>
<org.eventb.core.prProof name="unfold_node_c/inst_2_pat_c/INV"/>
<org.eventb.core.prProof name="apply_pattern/inst_2_pat_c/INV"/>
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<org.eventb.core.lang name="L"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Pat∈dom(components)∧components∈Model ⇸ ℙ(Component)∧Inst∈dom(components)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p22">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p25">
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</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p26">
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</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="1"/>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p27">
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c⦂Component·c∈dom(pat2inst_c)⇒pat2inst_c∈Component ⇸ ℙ(ℤ × Component)∧Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)∧c∈dom(c_multiplicity(Pat))∧c_multiplicity(Pat)∈Component ⇸ ℤ∧⊤∧⊤"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℕ"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c∈dom(pat2inst_c)⇒pat2inst_c∈Component ⇸ ℙ(ℤ × Component)∧Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)∧c∈dom(c_multiplicity(Pat))∧c_multiplicity(Pat)∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p28" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_clone_c∈components(Inst) ⇸ components(Pat)"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) → components(Inst)∪ran(new_c)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c0⦂Component·c0∈dom(pat2inst_c{c ↦ new_c})⇒(pat2inst_c{c ↦ new_c})(c0)∈1 ‥ c_multiplicity(Pat)(c0) → components(Inst)∪ran(new_c)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c0⦂Component·c0∈dom(pat2inst_c{c ↦ new_c})⇒(pat2inst_c{c ↦ new_c})(c0)∈1 ‥ c_multiplicity(Pat)(c0) → (components{Inst ↦ components(Inst)∪ran(new_c)})(Inst)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="c∈dom(pat2inst_c{c ↦ new_c})"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c0∈dom(pat2inst_c{c ↦ new_c})⇒(pat2inst_c{c ↦ new_c})(c0)∈1 ‥ c_multiplicity(Pat)(c0) → components(Inst)∪ran(new_c)">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="pat2inst_c(c0)∈1 ‥ c_multiplicity(Pat)(c0) → components(Inst)∪ran(new_c)">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="pat2inst_c∈components(Pat) ⇸ (ℕ ⇸ components(Inst))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c0) → components(Inst)∪ran(new_c)">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c0=c">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
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<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
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<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="components{Inst ↦ components(Inst)∪ran(new_c)}∈Model ⇸ ℙ(Component)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_clone_c∈components(Inst) ⇸ components(Pat)"/>
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<org.eventb.core.prPred name="p38" org.eventb.core.predicate="(container(Pat))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="pat2inst_c∈components(Pat) ⇸ (ℕ ⇸ components(Mdl)∪ran(new_components))"/>
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<org.eventb.core.prPred name="p63" org.eventb.core.predicate="pat2inst_c∈({Mdl} ⩤ components)(Pat) ⇸ (ℕ ⇸ (components{Mdl ↦ components(Mdl)∪ran(new_components)})(Inst))"/>
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<org.eventb.core.prPred name="p60" org.eventb.core.predicate="pat2inst_c∈components(Mdl)∪ran(new_components) ⇸ (ℕ ⇸ ({Mdl} ⩤ components)(Inst))"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="inst_components∈components(Mdl) ⤔ components(Mdl)">
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="pat2inst_c(c)∈1 ‥ c_multiplicity(Pat)(c) → (components{Mdl ↦ components(Mdl)∪ran(new_components)})(Inst)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c∪(ran(new_c) × {c}))⊆{c}"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(to_unfold_c ∖ {c})∩ran(inst2pat_c∪(ran(new_c) × {c}))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/pat2inst_clone/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2" org.eventb.core.prSets="Component">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p5"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="PP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p2,p1">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="ran({c} ⩤ to_clone_c)⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="ran(to_clone_c)⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_c/pat2inst_unfold/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prHyps="">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p0" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p1"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p2"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_node_c/pat2inst_clone/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p5"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p6"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p3,p2">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c∈dom(to_unfold_c_in)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="ran(to_clone_c∪(ran(new_c) × {c}))⊆dom(pat2inst_c{c ↦ new_c})"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="ran(to_clone_c)⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_node_c/pat2inst_unfold/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="SELECT0" org.eventb.core.prHyps="p1,p3,p4,p7,p29,p30,p8,p9,p10,p11,p12,p31,p32,p13,p14,p15,p16,p17,p33,p19,p20,p21,p22,p23,p24,p26,p27,p28"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(ran(new_c))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="to_clone_c⊆inst2pat_c">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c∪(ran(new_c) × {c}))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/pat2inst_unfold_in/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component">
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c∩dom(container)⊆{c}"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.lang name="L"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}))⊆dom(container)"/>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬Inst=Mdl">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components∈Model ↔ Component">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_node_c/unfold_root/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p33" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom((to_unfold_c_in ∖ {c ↦ dest})∪((container∼[{c}] ∖ c_multiplicity∼[{0}]) × ran(new_c)))⊆dom(container∪(ran(new_c) × {dest}))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/unfold_root/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="to_clone_c⊆inst2pat_c">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_unfold_c∩dom(container∪(new_components∼;container;(inst_components∪new_components)))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/unfold_in/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p10" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p11"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p12" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p13"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p14" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p15"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p16" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p17"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p18" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p19"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p20" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p21"/>
<org.eventb.core.prHypAction name="REWRITE6" org.eventb.core.prHidden="p22" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p23"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p24"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p25"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="PP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p9,p7,p8,p5,p2,p1,p6,p4,p3">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container∪(new_components∼;container;(inst_components∪new_components)))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="containers[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="ran(new_components)∩ran(containers)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="ran(new_components)∩ran(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="dom(inst_components) ◁ containers;inst_components⊆inst_components;containers"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="¬Inst=Mdl"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
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</org.eventb.core.prProof>
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<org.eventb.core.lang name="L"/>
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p3" org.eventb.core.prHyps=""/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="((container{Inst ↦ (∅ ⦂ ℙ(Component×Component))})(Pat))[ran(∅ ⦂ ℙ(Component×Component))]⊆ran(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
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<org.eventb.core.lang name="L"/>
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<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(container(Pat))[dom(pat2inst_c{c ↦ new_c})]⊆dom(pat2inst_c{c ↦ new_c})"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="(container(Pat))[dom(pat2inst_c)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩dom(container(Pat))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_node_c/pat2inst_cont/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38,p39,p40" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p44" org.eventb.core.prHyps="p43">
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with Pat=Inst" org.eventb.core.prHyps="p43">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p45" org.eventb.core.prInfHyps="p46"/>
<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p5" org.eventb.core.prInfHyps="p47"/>
<org.eventb.core.prHypAction name="DESELECT2" org.eventb.core.prHyps="p5,p45"/>
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p44" org.eventb.core.prHyps="p31,p8,p34,p3,p13,p26,p16,p25,p32,p20,p22,p17,p38,p14,p11,p18,p35,p24,p39,p28,p9,p1,p40,p36,p23,p6,p19,p2,p4,p30,p33,p5,p29,p27,p10,p21,p15,p7,p12,p41,p43,p47">
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<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container(Pat)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="Pattern⊆Model"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="Pat∈dom(container{Inst ↦ container(Inst)∪(ran(new_c) × {dest})})"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_clone_c⊆inst2pat_c∼"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container{Inst ↦ container(Inst)∪(ran(new_c) × {dest})}∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="Pat=Inst"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_clone_c∈components(Inst) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="dom(to_unfold_c_in)∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="¬Pat=Inst"/>
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<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="inst2pat_c∈components(Inst) → components(Pat)"/>
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<org.eventb.core.prPred name="p31" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀m⦂Model·container(m)∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p51" org.eventb.core.predicate="(container(Pat))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)">
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_unfold_c∩dom(container(Pat))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="Inst∈dom(container)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_unfold_c_in∈components(Pat) ↔ components(Inst)"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="(container(Inst))[dom(pat2inst_c)]⊆dom(pat2inst_c)">
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="(({Inst} ⩤ container)(Pat))[ran(inst2pat_c)]⊆ran(inst2pat_c)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container(Pat))"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="(container(Pat))[ran(inst2pat_c)]⊆ran(inst2pat_c)"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.funOvr:1"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/pat2inst_cont/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38,p39,p40" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p37" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p41"/>
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<org.eventb.core.prAnte name="'">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p44" org.eventb.core.prHyps="p43">
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with Pat=Mdl" org.eventb.core.prHyps="p43">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p45" org.eventb.core.prInfHyps="p46"/>
<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p45"/>
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p44" org.eventb.core.prHyps="p30,p7,p33,p3,p10,p26,p13,p25,p31,p21,p22,p14,p38,p11,p9,p15,p35,p24,p39,p27,p8,p1,p40,p36,p23,p5,p16,p2,p4,p29,p32,p19,p17,p12,p18,p6,p28,p34,p20,p41,p43">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p48" org.eventb.core.prHyps="p47">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p29">
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container(Pat)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="(container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components)))[ran(inst2pat_c)]⊆ran(inst2pat_c)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="(container(Mdl))∼;inst_components∼;container(Inst)⊆inst_components∼"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_clone_c⊆inst2pat_c∼"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Inst) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="((container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))})(Pat))[ran(inst2pat_c)]⊆ran(inst2pat_c)"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="Pat=Mdl"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Mdl∈dom(container)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="Mdl∈dom(components)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))}∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="(container(Pat))[dom(pat2inst_c)]⊆dom(pat2inst_c)">
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="inst2pat_c∈components(Inst) → components(Pat)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀m⦂Model·container(m)∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="inst_components∈components(Inst) ⤔ components(Mdl)"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="(({Mdl} ⩤ container)(Pat))[ran(inst2pat_c)]⊆ran(inst2pat_c)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c∩dom(container(Pat))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="(container(Mdl))[dom(pat2inst_c)]⊆dom(pat2inst_c)">
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Inst∈dom(container)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="to_unfold_c_in∈components(Pat) ↔ components(Inst)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container(Pat))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="inst_components∼;container(Inst);inst_components⊆container(Mdl)"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="¬Pat=Mdl"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="new_components∈components(Inst) ∖ dom(inst_components) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="(container(Pat))[ran(inst2pat_c)]⊆ran(inst2pat_c)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="Pat∈dom(container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))})"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="clone_cont/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pat∈dom(container)"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p51" org.eventb.core.predicate="(({Inst} ⩤ container)(Pat))∼[ran(to_clone_c∪(ran(new_c) × {c}))]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="x∈(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c})">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Inst)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p61" org.eventb.core.predicate="¬x∈(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c})">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀m⦂Model·container(m)∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="(container(Pat))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="pat2inst_c∈components(Pat) ⇸ (ℕ ⇸ components(Inst))"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="∀x⦂Component·x∈(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c})⇒x∈(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p58" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c})⊆(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_unfold_c∩dom(container(Pat))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="((container(Pat))∼[ran(to_clone_c)]∪(container(Pat))∼[ran(ran(new_c) × {c})])∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container{Inst ↦ container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)})}∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈dom(container{Inst ↦ container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)})})"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)∪ran(ran(new_c) × {c})]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="x ↦ x0∈pat2inst_c{c ↦ new_c}">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="((container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c}))∪((container(Pat))∼[ran(ran(new_c) × {c})]∩dom(pat2inst_c{c ↦ new_c}))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="(container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)}))∼[ran(to_clone_c∪(ran(new_c) × {c}))]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="x∈dom(pat2inst_c{c ↦ new_c})">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="Inst∈dom(container)"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p69" org.eventb.core.predicate="x=c">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container(Pat))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="ran(to_clone_c)⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p75" org.eventb.core.predicate="(container(Pat))∼[ran(ran(new_c) × {c})]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p68" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="⊥"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="∃x0⦂ℙ(ℤ×Component)·x ↦ x0∈pat2inst_c{c ↦ new_c}">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="((container{Inst ↦ container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)})})(Pat))∼[ran(to_clone_c∪(ran(new_c) × {c}))]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="c∈(container(Pat))∼[ran(to_clone_c)]"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="x∈(container(Pat))∼[ran(to_clone_c)]">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Pat))∼[ran(to_clone_c)]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p74" org.eventb.core.predicate="(∅ ⦂ ℙ(Component))⊆(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c})"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c∪(ran(new_c) × {c}))]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p56" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))∧(container(Pat))∼[ran(ran(new_c) × {c})]∩dom(pat2inst_c{c ↦ new_c})=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀c⦂Component·c∈dom(pat2inst_c)⇒pat2inst_c(c)∈1 ‥ c_multiplicity(Pat)(c) → components(Inst)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p76" org.eventb.core.predicate="container(Pat)∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="Pat"/>
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<org.eventb.core.prReas name="r18" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.relImgUnionRightRewrites"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.unionInterDistRewrites"/>
<org.eventb.core.prReas name="r12" org.eventb.core.prRID="org.eventb.core.seqprover.ri"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
<org.eventb.core.prReas name="r19" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r16" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.funOvr:1"/>
<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r20" org.eventb.core.prRID="org.eventb.core.seqprover.allD"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
<org.eventb.core.prReas name="r14" org.eventb.core.prRID="org.eventb.core.seqprover.contrL1"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.domRanUnionDistRewrites"/>
<org.eventb.core.prReas name="r11" org.eventb.core.prRID="org.eventb.core.seqprover.setEqlRewrites"/>
<org.eventb.core.prReas name="r13" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
<org.eventb.core.prReas name="r15" org.eventb.core.prRID="org.eventb.core.seqprover.rmL1"/>
<org.eventb.core.prReas name="r10" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/clone_cont/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38,p39,p40,p41,p42,p43,p44,p45" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p42" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p46"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p47"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ovr in goal" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p49" org.eventb.core.prHyps="p48">
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with Pat=Mdl" org.eventb.core.prHyps="p48">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p10" org.eventb.core.prInfHyps="p50"/>
<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p10"/>
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p49" org.eventb.core.prHyps="p33,p8,p37,p3,p11,p30,p14,p29,p34,p24,p25,p16,p43,p12,p9,p15,p40,p27,p44,p38,p31,p18,p21,p2,p6,p45,p41,p17,p1,p4,p28,p10,p36,p26,p5,p35,p22,p19,p13,p20,p7,p32,p39,p23,p46,p48,p50">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p52" org.eventb.core.prHyps="p51">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Functional image simplification in goal" org.eventb.core.prGoal="p52" org.eventb.core.prHyps="p30">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p10">
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</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="0.0.0.0"/>
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<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="0.0.0.0"/>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_unfold_c∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="(container(Mdl))∼;inst_components∼;container(Inst)⊆inst_components∼"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Inst) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c_in∈components(Pat) ⇸ components(Inst)"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="Pat=Mdl"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈dom(container)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="dom(to_unfold_c_in)∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Mdl∈dom(components)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))}∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="(({Mdl} ⩤ container)(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="(container(Pat))[dom(pat2inst_c)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀m⦂Model·container(m)∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="inst_components∈components(Inst) ⤔ components(Mdl)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="(container(Pat))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="pat2inst_c∈components(Pat) ⇸ (ℕ ⇸ components(Inst))"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prReas name="r10" org.eventb.core.prRID="org.eventb.core.seqprover.allD"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.relImgUnionRightRewrites"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.domRanUnionDistRewrites"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.cut"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p49" org.eventb.core.predicate="Pattern⊆Model"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
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<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_unfold_c_in∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="Pat=Inst"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_clone_c∈components(Inst) ⇸ components(Pat)"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="(container(Inst))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="¬Pat=Inst"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="(container(Pat))[dom(pat2inst_c)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p39" org.eventb.core.predicate="pat2inst_c∈components(Pat) ⇸ (ℕ ⇸ components(Inst))"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Pat∈dom(container{Inst ↦ container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)})})"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Inst∈dom(container)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container(Pat))"/>
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<org.eventb.core.prPred name="p51" org.eventb.core.predicate="(container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)}))[dom(to_unfold_c_in) ∖ {c}]⊆dom(pat2inst_c{c ↦ new_c})"/>
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<org.eventb.core.prPred name="p47" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Pat))∼[to_unfold_c]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀c⦂Component·c∈dom(pat2inst_c)⇒pat2inst_c(c)∈1 ‥ c_multiplicity(Pat)(c) → components(Inst)"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="Pat∈dom(container)"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.funOvr:1"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
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<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p36"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p48" org.eventb.core.predicate="dom(to_unfold_c_in)∩((container{Inst ↦ container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)})})(Pat))∼[to_unfold_c]⊆{c}"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Inst)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀m⦂Model·container(m)∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="(container(Pat))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="pat2inst_c∈components(Pat) ⇸ (ℕ ⇸ components(Inst))"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Pat))∼[dom(to_unfold_c_in)]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_unfold_c∩dom(container(Pat))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="container{Inst ↦ container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)})}∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="Pat∈dom(container{Inst ↦ container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)})})"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Inst∈dom(container)"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Inst))∼[to_unfold_c]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container(Pat))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="ran(to_clone_c)⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="dom(to_unfold_c_in)∩(({Inst} ⩤ container)(Pat))∼[to_unfold_c]⊆{c}"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Inst)∪(ran(new_c) × {to_unfold_c_in(c)}))∼[to_unfold_c]⊆{c}"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Pat))∼[to_unfold_c]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀c⦂Component·c∈dom(pat2inst_c)⇒pat2inst_c(c)∈1 ‥ c_multiplicity(Pat)(c) → components(Inst)"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p49" org.eventb.core.prHyps="p48">
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<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p26" org.eventb.core.prInfHyps="p50"/>
<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p26"/>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="pat2inst_c" org.eventb.core.type="ℙ(Component×ℙ(ℤ×Component))"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="Pattern⊆Model"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="(container(Mdl))∼;inst_components∼;container(Inst)⊆inst_components∼"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m⦂Model·container(m)∈components(m) ⇸ components(m)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_clone_c∈components(Inst) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c_in∈components(Pat) ⇸ components(Inst)"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="Pat=Mdl"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Mdl∈dom(container)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="dom(to_unfold_c_in)∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Mdl∈dom(components)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))}∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="(container(Pat))[dom(pat2inst_c)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p36" org.eventb.core.predicate="(container(Pat))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)"/>
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<org.eventb.core.prPred name="p40" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="inst_components∼;container(Inst);inst_components⊆container(Mdl)"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))}∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(to_unfold_c_in)∩((container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))})(Pat))∼[dom(to_unfold_c_in)]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_index)⇒c_index(c)∈1 ‥ c_multiplicity(Pat)(to_clone_c(c))"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="(container(Pat))[dom(pat2inst_c)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components)))∼[dom(to_unfold_c_in)]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="dom(to_unfold_c_in)∩(({Mdl} ⩤ container)(Pat))∼[dom(to_unfold_c_in)]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀m⦂Model·∃f⦂ℙ(Component×Component)·container(m)⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀m⦂Model·container(m)∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="inst_components∈components(Inst) ⤔ components(Mdl)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="(container(Pat))[dom(to_unfold_c_in)]⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="pat2inst_c∈components(Pat) ⇸ (ℕ ⇸ components(Inst))"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Pat))∼[dom(to_unfold_c_in)]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_unfold_c∩dom(container(Pat))=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="(container(Pat))∼[ran(to_clone_c)]∩dom(pat2inst_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Inst∈dom(container)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container(Pat))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="ran(to_clone_c)⊆dom(pat2inst_c)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="inst_components∼;container(Inst);inst_components⊆container(Mdl)"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="dom(to_unfold_c_in)∩(container(Pat))∼[to_unfold_c]=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="¬Pat=Mdl"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀c⦂Component·c∈dom(pat2inst_c)⇒pat2inst_c(c)∈1 ‥ c_multiplicity(Pat)(c) → components(Inst)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="new_components∈components(Inst) ∖ dom(inst_components) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="Pat∈dom(container{Mdl ↦ container(Mdl)∪((inst_components∪new_components)∼;container(Inst);(inst_components∪new_components))})"/>
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<org.eventb.core.prPred name="p45" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_clone/THM" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21" org.eventb.core.prSets="Component,Model">
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_clone_c⊆inst2pat_c"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(to_unfold_c_in∪(container∼[{to_clone_c(c)}] × {c}));inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="Pat∈Pattern">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_clone_c⊆inst2pat_c">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="inst2pat_c∪(ran(new_c) × {c})∈(components∪({Inst} × ran(new_c)))[{Inst}] → (components∪({Inst} × ran(new_c)))[{Pat}]"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="Inst∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_node_c/inst2pat2_clone/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p5"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p7"/>
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<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p9"/>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Model×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_clone_c⊆(inst2pat_c∪(ran(new_c) × {c}))∼∧ran(new_c) × {c}⊆(inst2pat_c∪(ran(new_c) × {c}))∼"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="ran(new_c) × {c}⊆(inst2pat_c∪(ran(new_c) × {c}))∼"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_clone_c⊆inst2pat_c∼"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_clone_c∪(ran(new_c) × {c})⊆(inst2pat_c∪(ran(new_c) × {c}))∼"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(Pat)(c) ↣ Component ∖ union(ran(components))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_clone_c⊆(inst2pat_c∪(ran(new_c) × {c}))∼"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_node_c/inst2pat_unfold_in/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="((to_unfold_c_in ∖ {c ↦ dest})∪((container∼[{c}] ∖ c_multiplicity∼[{0}]) × ran(new_c)));(inst2pat_c∪(ran(new_c) × {c}))⊆container∪(ran(new_c) × {dest})"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(ran(new_c))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="to_clone_c⊆inst2pat_c">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="apply_pattern/inst2pat_c_ty/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26">
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<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="to_clone_c⊆inst2pat_c">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="inst2pat_c∈(components∪({Mdl} × ran(new_components)))[{Inst}] → (components∪({Mdl} × ran(new_components)))[{Pat}]"/>
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<org.eventb.core.prPred name="p22" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container∪(new_components∼;container;(inst_components∪new_components))"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="containers[dom(inst_components)]⊆dom(inst_components)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="ran(new_components)∩ran(containers)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="dom(inst_components) ◁ containers;inst_components⊆inst_components;containers"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="¬Inst=Mdl"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Inst∈Model"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Inst∈dom(container)"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))">
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pat∈dom(container)"/>
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<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
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<org.eventb.core.prProof name="instanciate_pattern/inst2pat_cont/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p9" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p10"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p11" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p12"/>
<org.eventb.core.prHypAction name="REWRITE6" org.eventb.core.prHidden="p13" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p14"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p15" org.eventb.core.prHyps=""/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(Component×Component));(components[{Inst}] ⩤ container)=components[{Inst}] ⩤ container;(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_root_c/inst2pat_unfold_in/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(ran(new_c))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="to_unfold_c∩ran(to_clone_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="to_clone_c⊆inst2pat_c">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(to_unfold_c_in∪((container∼[{c}] ∖ c_multiplicity∼[{0}]) × ran(new_c)));(inst2pat_c∪(ran(new_c) × {c}))⊆container"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]">
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_root_c/inst2pat_cont/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prReas name="r13" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬Inst=Mdl">
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="components∈Model ↔ Component"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_root_c/cm/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c∈to_unfold_c"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_clone_c∈components[{Inst}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="c_multiplicity∈(components∪({Inst} × ran(new_c)))[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="components∈Model ↔ Component"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p13,p28,p4,p2,p26,p11,p30,p18,p31,p8,p10,p5,p19,p7,p17,p22,p20,p9,p29,p14,p1,p21,p16,p15,p3,p6,p23,p12,p25,p27,p24">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="Inst≠Mdl"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(components∪({Inst} × ran(new_c)))∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
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<org.eventb.core.prProof name="unfold_root_c/c_mult/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
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<org.eventb.core.prProof name="unfold_node_c/c_mult/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)">
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p74" org.eventb.core.predicate="c∈to_unfold_c">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀c⦂Component,s⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧s ↦ c∈containers∪(id ⦂ ℙ(Component×Component))∧m∈ran(c_indexes)⇒¬s∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧¬m∈ran(c_indexes)∧s∈dom(e)⇒¬e∈ran(c_indexes)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧¬(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈ran(c_indexes)⇒¬m∈ran(c_indexes)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒c_indexes(i)=inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index)">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p47" org.eventb.core.predicate="container⊆containers">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0">
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p51" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p69" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p75" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="P=components[{Pat}]"/>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p58" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p59" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p61" org.eventb.core.predicate="containers;containers⊆containers">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])">
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="finite(components[{Pat}])"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p63" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])">
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<org.eventb.core.prPred name="p64" org.eventb.core.predicate="c∈dom(c_multiplicity)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧m∉ran(c_indexes)∧s∈dom(e)⇒e∉ran(c_indexes)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="Inst∈Model ∖ Pattern">
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prProof name="unfold_node_c/new_c_fin/THM" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="todo∈components[{Pat}] → ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
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<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))">
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<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c∈dom(todo)∧todo∈Component ⇸ ℙ(ℙ(Component × ℤ))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="¬Inst=Mdl">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈components[{Pat}]∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="todo_clone/WD" org.eventb.core.confidence="0" org.eventb.core.prFresh="c" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p33">
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_clone_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="Pattern⊆Model"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="c∈dom(todo)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p11" org.eventb.core.predicate="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="c∈ran(to_clone_c)⇒c∈dom(todo)∧todo∈Component ⇸ ℤ∧finite(to_clone_c∼[{c}])">
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_clone_c⊆inst2pat_c"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="c∈ran(to_clone_c)">
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="todo∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Inst≠Mdl"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="todo∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c⇒todo(c)=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="todo_unfold_in/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="c" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p32">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p34" org.eventb.core.prHyps="p33">
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<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒ran(c_mult)≠(∅ ⦂ ℙ(ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult)⇒b≥x)"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="c_mult=c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="(λc⦂Component·c∈components[{Pat}] ∣ ((components[{Pat}] ∖ dom(container))∩{c}) × (containers∼[{c}] ∖ components[{Inst}] → 0 ‥ max(ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}))))∈({Inst} ⩤ components)[{Pat}] → (Component ↔ (({Inst} ⩤ components)[{Pat}] ⇸ ℕ))"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="c_mult_others∈components[{Pat}] ∖ dom(inst_components) → ℕ"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒¬(c_mult_others=(∅ ⦂ ℙ(Component×ℤ))∧(∀pc⦂Component·¬pc∈dom(inst_components)))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})⇒b≥x)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="∀c⦂Component,s⦂Component·s ↦ c∈container⇒todo'(s)=todo'(c)∗c_mult(s)">
<org.eventb.core.prIdent name="todo'" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒todo(c)=((to_unfold_c∩{c})∪to_unfold_c_in[{c}]) × weight(c)"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.rmL1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/todo_fin/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p5"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬(∀sc·¬(sc⊆ℕ × components[{Pat}]∧(∀c·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+c_mult(c) × {c}⊆sc)∧(∀i,c,s·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_mult(s) × {s}⊆sc)))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p6"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬¬([[0]]⊆ℕ × components[{Pat}]∧(∀c·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+c_mult(c) × {c}⊆[[1]])∧(∀i,c,s·i ↦ c∈[[3]]∧s ↦ c∈container⇒1 ‥ i∗c_mult(s) × {s}⊆[[3]]))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p6" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p7"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p7"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p8"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p9"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p10" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p11"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p11" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p12"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with c_mult=c_mult_others{pc·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p14">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p7" org.eventb.core.prInfHyps="p13"/>
<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p7"/>
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∃ hyp (∃sc·sc⊆ℕ × components[{Pat}]∧(∀c·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+(c_mult_others{pc·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(c) × {c}⊆sc)∧(∀i,c,s·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗(c_mult_others{pc·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(s) × {s}⊆sc))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p13" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p15,p16,p17">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prHypAction>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p15,p16,p17"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="1"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue=""/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_mult_others" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(s) × {s}⊆sc">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="finite(inter({sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(c) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(s) × {s}⊆sc) ∣ sc}))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="¬(∀sc⦂ℙ(ℤ×Component)·¬(sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+c_mult(c) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_mult(s) × {s}⊆sc)))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c_mult=c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="{sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+c_mult(c) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_mult(s) × {s}⊆sc) ∣ sc}≠(∅ ⦂ ℙ(ℙ(ℤ×Component)))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∃sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(c) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(s) × {s}⊆sc)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∃sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+c_mult(c) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_mult(s) × {s}⊆sc)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(c) × {c}⊆sc">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="finite(inter({sc⦂ℙ(ℤ×Component)·sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+c_mult(c) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_mult(s) × {s}⊆sc) ∣ sc}))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∃sc⦂ℙ(ℤ×Component)·¬¬(sc⊆ℕ × components[{Pat}]∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒1 ‥ 1+c_mult(c) × {c}⊆sc)∧(∀i⦂ℤ,c⦂Component,s⦂Component·i ↦ c∈sc∧s ↦ c∈container⇒1 ‥ i∗c_mult(s) × {s}⊆sc))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="sc⊆ℕ × components[{Pat}]">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/todo_unfold/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="generalized MP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p0">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p1" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p2"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p7"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊥ hyp" org.eventb.core.prHyps="p7"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo'" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀c⦂Component·c∉dom(container)∧c∉to_unfold_c⇒todo(c)=0">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="todo'∈components[{Pat}] → ℕ∧⊥∧(∀c⦂Component,s⦂Component·s ↦ c∈container⇒todo'(s)=todo'(c)∗c_mult(s))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="⊥"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂Component·¬c∈dom(container)∧¬c∈to_unfold_c⇒todo(c)=0">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒todo'(c)=c_mult(c)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="todo'∈components[{Pat}] → ℕ∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒todo'(c)=c_mult(c))∧(∀c⦂Component,s⦂Component·s ↦ c∈container⇒todo'(s)=todo'(c)∗c_mult(s))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.falseHyp"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4,p5,p6"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p7" org.eventb.core.prHyps=""/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="todo'∈components[{Pat}] → ℕ">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="M=max(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="k∈1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p101" org.eventb.core.predicate="∀k0⦂ℤ·¬k0∈1 ‥ max(ran(c_multiplicity))∨¬c_indexes(dest){c ↦ k0}=(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p11" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p85" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p100" org.eventb.core.predicate="∀k0⦂ℤ·¬(k0∈1 ‥ max(ran(c_multiplicity))∧c_indexes(dest){c ↦ k0}=(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c0⦂Component,i⦂Component,k⦂ℤ·c0 ↦ i∈(to_unfold_c_in ∖ {c ↦ dest})∪((container∼[{c}] ∖ c_multiplicity∼[{0}]) × ran(new_c))∧k∈1 ‥ M⇒(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k}∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k}∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ M)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k}∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒c_indexes(i)=inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index)"/>
<org.eventb.core.prPred name="p76" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p79" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k}∈todo">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p40" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p98" org.eventb.core.predicate="¬(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k}∈{k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p93" org.eventb.core.predicate="i∈ran(new_c)">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p44" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p84" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p88" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p89" org.eventb.core.predicate="i=c">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p61" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p69" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
<org.eventb.core.prIdent name="b" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p82" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p91" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(c){c0 ↦ k}∈todo">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p83" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="k∈1 ‥ M">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p86" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="c0 ↦ i∈(to_unfold_c_in ∖ {c ↦ dest})∪((container∼[{c}] ∖ c_multiplicity∼[{0}]) × ran(new_c))∧k∈1 ‥ M⇒(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k}∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈P∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p99" org.eventb.core.predicate="¬(∃k0⦂ℤ·k0∈1 ‥ max(ran(c_multiplicity))∧c_indexes(dest){c ↦ k0}=(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i){c0 ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p94" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p77" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
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<org.eventb.core.prPred name="p32" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p75" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p95" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
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<org.eventb.core.prPred name="p42" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p78" org.eventb.core.predicate="todo∈components[{Pat}] → ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p80" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i)∪{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p87" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p96" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p92" org.eventb.core.predicate="¬i=c">
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<org.eventb.core.prPred name="p81" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="c0 ↦ i∈(to_unfold_c_in ∖ {c ↦ dest})∪((container∼[{c}] ∖ c_multiplicity∼[{0}]) × ran(new_c))">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p73" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p56" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i){c ↦ k}∈todo"/>
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<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
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<org.eventb.core.prPred name="p125" org.eventb.core.predicate="(inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}⊆(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ ((inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p105" org.eventb.core.predicate="¬(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})∈{k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p114" org.eventb.core.predicate="¬⊥"/>
<org.eventb.core.prPred name="p116" org.eventb.core.predicate="dest∈dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p142" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ ((inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k})∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p108" org.eventb.core.predicate="∀k0⦂ℤ·¬k0∈1 ‥ M∨¬c_indexes(dest){c ↦ k0}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p113" org.eventb.core.predicate="¬c_indexes(dest){c ↦ k}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p98" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="c0∈P">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p103" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p110" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="m∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p92" org.eventb.core.predicate="⊥"/>
<org.eventb.core.prPred name="p102" org.eventb.core.predicate="c_indexes(dest){c ↦ k}∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p139" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ (c_indexes(dest){c ↦ k})∈todo">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p115" org.eventb.core.predicate="c_indexes(dest){c ↦ k}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="m∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p135" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ ((inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k})∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ (inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}}">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p106" org.eventb.core.predicate="¬(∃k0⦂ℤ·k0∈1 ‥ M∧c_indexes(dest){c ↦ k0}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k}))">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p96" org.eventb.core.predicate="c_indexes(dest){c ↦ k}=m">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p61" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
<org.eventb.core.prIdent name="b" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p120" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ ((inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k})∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ (inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="∀c0⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c0∈P∧s ↦ c0∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∧m∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}⇒m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}"/>
<org.eventb.core.prPred name="p121" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ m∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ (inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p88" org.eventb.core.predicate="∀k⦂ℤ·¬(k∈1 ‥ max(ran(c_multiplicity))∧c_indexes(dest){c ↦ k}=m)">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p80" org.eventb.core.predicate="c0∈components[{Pat}]">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p126" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ ((inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k})∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p75" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p97" org.eventb.core.predicate="c_indexes(dest){c ↦ k}∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p111" org.eventb.core.predicate="¬k∈1 ‥ max(ran(c_multiplicity))∨¬c_indexes(dest){c ↦ k}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p89" org.eventb.core.predicate="∀k⦂ℤ·¬k∈1 ‥ max(ran(c_multiplicity))∨¬c_indexes(dest){c ↦ k}=m">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p58" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p76" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p112" org.eventb.core.predicate="¬⊤∨¬c_indexes(dest){c ↦ k}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k})">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p84" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p144" org.eventb.core.predicate="¬c∈ran(new_c)"/>
<org.eventb.core.prPred name="p93" org.eventb.core.predicate="¬¬k∈1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p127" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ ((inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k})∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p119" org.eventb.core.predicate="(inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p99" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p146" org.eventb.core.predicate="¬c0=c">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p132" org.eventb.core.predicate="s ↦ c∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀m⦂ℙ(Component×ℤ),p⦂Component·m∈todo∧p∈dom(m)⇒containers[{p}]⊆dom(m)"/>
<org.eventb.core.prPred name="p94" org.eventb.core.predicate="¬¬c_indexes(dest){c ↦ k}=m">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c0⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c0∈P∧s ↦ c0∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∧m∈((containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}]))∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧((containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}]))∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}⇒m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}"/>
<org.eventb.core.prPred name="p133" org.eventb.core.predicate="c∈components[{Pat}]"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p77" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i)∪{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p100" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p141" org.eventb.core.predicate="∀k0⦂ℤ·¬k0∈1 ‥ max(ran(c_multiplicity))∨¬c_indexes(dest){c ↦ k0}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ (c_indexes(dest){c ↦ k})">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p42" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p91" org.eventb.core.predicate="¬(¬k∈1 ‥ max(ran(c_multiplicity))∨¬c_indexes(dest){c ↦ k}=m)">
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<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p43" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p118" org.eventb.core.predicate="(inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}=m">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p78" org.eventb.core.predicate="m∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p68" org.eventb.core.predicate="m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p73" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ m∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p69" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i)∪{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p136" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ (inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}}">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p147" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ ((inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k})⊆(inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{dest}] ◁ c_index)){c ↦ k}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p101" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
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<org.eventb.core.prPred name="p48" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p74" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p85" org.eventb.core.predicate="m∈todo">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p62" org.eventb.core.predicate="s∈P∧c0∈P∧s ↦ c0∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∧m∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}⇒m∈todo ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p67" org.eventb.core.predicate="s ↦ c0∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])">
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<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p81" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p107" org.eventb.core.predicate="∀k0⦂ℤ·¬(k0∈1 ‥ M∧c_indexes(dest){c ↦ k0}=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{c0}] ◁ (c_indexes(dest){c ↦ k}))">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p63" org.eventb.core.predicate="s∈P">
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<org.eventb.core.prPred name="p55" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
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<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r17" org.eventb.core.prRID="org.eventb.core.seqprover.doCase"/>
<org.eventb.core.prReas name="r16" org.eventb.core.prRID="org.eventb.core.seqprover.setEqlRewrites"/>
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<org.eventb.core.prReas name="r10" org.eventb.core.prRID="org.eventb.core.seqprover.contrL1"/>
<org.eventb.core.prReas name="r11" org.eventb.core.prRID="org.eventb.core.seqprover.he:1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
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<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r13" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.rmL1"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="dest∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒dom(c_indexes(i))=(containers∪(id ⦂ ℙ(Component×Component)))[{inst2pat_c(i)}]"/>
<org.eventb.core.prPred name="p58" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
<org.eventb.core.prIdent name="b" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="finite(ran(new_c))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p61" org.eventb.core.predicate="k∈1 ‥ M⇒dest∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)">
<org.eventb.core.prIdent name="k" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p77" org.eventb.core.predicate="c_indexes∈Component ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p69" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="M=max(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="k∈1 ‥ M">
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<org.eventb.core.prPred name="p67" org.eventb.core.predicate="k∈1 ‥ max(ran(c_multiplicity))">
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p75" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀k⦂ℤ·k∈1 ‥ M⇒dest∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)"/>
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<org.eventb.core.prPred name="p74" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
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<org.eventb.core.prPred name="p30" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒c_indexes(i)=inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i)∪{c ↦ k}∈todo"/>
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<org.eventb.core.prPred name="p36" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
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<org.eventb.core.prPred name="p38" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
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<org.eventb.core.prPred name="p43" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i)∪{c ↦ k}∈todo"/>
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<org.eventb.core.prPred name="p45" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="Inst≠Mdl"/>
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<org.eventb.core.prPred name="p68" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
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<org.eventb.core.prPred name="p73" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p56" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(Component×ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
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<org.eventb.core.prPred name="p33" org.eventb.core.predicate="∀c⦂Component·c∈dom(c_multiplicity)⇒todo(c)=c_multiplicity(c)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p38" org.eventb.core.predicate="f;f⊆f">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p80" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i)∪{c ↦ k}∈todo(c)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p123" org.eventb.core.predicate="(containers[{c}]∪(∅ ⦂ ℙ(Component))∪{c}) ◁ m∈todo(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p125" org.eventb.core.predicate="(containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components))∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p89" org.eventb.core.predicate="s∈components[{Pat}]">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p76" org.eventb.core.predicate="m∈(containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components))∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p99" org.eventb.core.predicate="(new_components∼;containers;inst_components;containers)[{s}]=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p118" org.eventb.core.predicate="¬c∈dom(new_components∼;containers;inst_components;containers)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ M)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒c_indexes(i)=inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index)"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="((containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components)))∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p92" org.eventb.core.predicate="m∈containers[{s}]∪(new_components∼;containers;inst_components;containers)[{s}]∪(new_components∼;containers;(new_components∪inst_components))[{s}]∪{s} ⇸ 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p74" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo(c)⇒m∈todo(s)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p85" org.eventb.core.predicate="m∈containers[{s}]∪(new_components∼;containers;inst_components;containers)[{s}]∪(new_components∼;containers;(new_components∪inst_components))[{s}]∪(id ⦂ ℙ(Component×Component))[{s}] → 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p124" org.eventb.core.predicate="(containers[{c}]∪{c}) ◁ m∈todo(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p122" org.eventb.core.predicate="¬c∈dom(new_components∼;containers;(new_components∪inst_components))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p107" org.eventb.core.predicate="m∈containers[{s}]∪(∅ ⦂ ℙ(Component))∪(∅ ⦂ ℙ(Component))∪{s} ⇸ 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p113" org.eventb.core.predicate="¬c∈dom(new_components∼)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p97" org.eventb.core.predicate="¬s∈dom(new_components∼)">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p105" org.eventb.core.predicate="dom(m)=containers[{s}]∪(new_components∼;containers;(new_components∪inst_components))[{s}]∪{s}">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p87" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo(c)⇒m∈todo(s)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p94" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p126" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p116" org.eventb.core.predicate="(containers[{c}]∪(new_components∼;containers;inst_components;containers)[{c}]∪(new_components∼;containers;(new_components∪inst_components))[{c}]∪{c}) ◁ m∈todo(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p109" org.eventb.core.predicate="m∈containers[{s}]∪{s} ⇸ 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p86" org.eventb.core.predicate="m∈containers[{s}]∪(new_components∼;containers;inst_components;containers)[{s}]∪(new_components∼;containers;(new_components∪inst_components))[{s}]∪{s} → 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p106" org.eventb.core.predicate="¬s∈dom(new_components∼;containers;(new_components∪inst_components))">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p104" org.eventb.core.predicate="m∈containers[{s}]∪(new_components∼;containers;(new_components∪inst_components))[{s}]∪{s} ⇸ 1 ‥ max(ran(c_multiplicity))">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p88" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo(c)⇒m∈todo(s)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p103" org.eventb.core.predicate="(new_components∼;containers;(new_components∪inst_components))[{s}]=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p58" org.eventb.core.predicate="s∈P∧c∈P∧s ↦ c∈containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components))∧m∈((containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components)))∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧((containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components)))∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p121" org.eventb.core.predicate="(new_components∼;containers;(new_components∪inst_components))[{c}]=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="m∈(containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components))∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p73" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
<org.eventb.core.prIdent name="b" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="s ↦ c∈containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p120" org.eventb.core.predicate="(containers[{c}]∪(new_components∼;containers;(new_components∪inst_components))[{c}]∪{c}) ◁ m∈todo(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p114" org.eventb.core.predicate="¬c∈ran(new_components)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∈todo(c)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p117" org.eventb.core.predicate="(new_components∼;containers;inst_components;containers)[{c}]=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p79" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo(c)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p93" org.eventb.core.predicate="dom(m)=containers[{s}]∪(new_components∼;containers;inst_components;containers)[{s}]∪(new_components∼;containers;(new_components∪inst_components))[{s}]∪{s}">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p98" org.eventb.core.predicate="¬s∈ran(new_components)">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈P∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p78" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p82" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈components[{Pat}]∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p112" org.eventb.core.predicate="c∈ran(new_components)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p90" org.eventb.core.predicate="c∈components[{Pat}]">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p75" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo(c)⇒m∈todo(s)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="m∈((containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components)))∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components))∧m∈((containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components)))∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧((containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components)))∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p95" org.eventb.core.predicate="s∈dom(new_components∼)">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p96" org.eventb.core.predicate="s∈ran(new_components)">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p119" org.eventb.core.predicate="(containers[{c}]∪(∅ ⦂ ℙ(Component))∪(new_components∼;containers;(new_components∪inst_components))[{c}]∪{c}) ◁ m∈todo(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p84" org.eventb.core.predicate="todo∈components[{Pat}] → ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p102" org.eventb.core.predicate="dom(m)=containers[{s}]∪(∅ ⦂ ℙ(Component))∪(new_components∼;containers;(new_components∪inst_components))[{s}]∪{s}">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p127" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="c∈P">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p77" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p68" org.eventb.core.predicate="(containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components))∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="m∈todo">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p111" org.eventb.core.predicate="c∈dom(new_components∼)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p81" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="s∈P">
<org.eventb.core.prIdent name="s" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.core.seqprover.doCase"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.relImgUnionLeftRewrites"/>
<org.eventb.core.prReas name="r12" org.eventb.core.prRID="org.eventb.core.seqprover.cut"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r11" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r10" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.rmL1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/todo/FIS" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p4"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p5"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p6" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p7"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with c_mult=c_mult_others{pc·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p9"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_mult_others" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·⊤∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∃todo'⦂ℙ(Component×ℤ)·todo'∈components[{Pat}] → ℕ∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒todo'(c)=(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(c))∧(∀c⦂Component,s⦂Component·s ↦ c∈container⇒todo'(s)=todo'(c)∗(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})(s))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∃f⦂ℙ(Component×Component)·f∈Component ↔ Component∧container⊆f∧f;f⊆f∧(id ⦂ ℙ(Component×Component))∩f=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∃todo'⦂ℙ(Component×ℤ)·todo'∈components[{Pat}] → ℕ∧(∀c⦂Component·c∈components[{Pat}] ∖ dom(container)⇒todo'(c)=c_mult(c))∧(∀c⦂Component,s⦂Component·s ↦ c∈container⇒todo'(s)=todo'(c)∗c_mult(s))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="c_mult=c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="todo_root/WD" org.eventb.core.confidence="0" org.eventb.core.prFresh="c" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27" org.eventb.core.prSets="Component,Model">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p17" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p28"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p29"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p30"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p31"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p31" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p32"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∀ goal (frees c)" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p33">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⇒ goal" org.eventb.core.prGoal="p33" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p35" org.eventb.core.prHyps="p34">
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p35" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p36">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p36" org.eventb.core.prHyps="p1,p2,p34,p3,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p18,p19,p20,p21,p22,p23,p32,p24,p25,p26,p27,p28">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p37">
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p37" org.eventb.core.prHyps="p19"/>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p38">
<org.eventb.core.prRule name="r7" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∃ hyp (∃f·container⊆f∧f;f⊆f∧id∩f=∅)" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p32" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p39,p40,p41">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prHypAction>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p39,p40,p41"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="*" org.eventb.core.prGoal="p42">
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p42" org.eventb.core.prHyps="p11"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p9" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p10"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p11" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p12"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="⊤"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p26" org.eventb.core.predicate="containers;containers⊆containers"/>
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<org.eventb.core.prPred name="p30" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p34" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prProof name="instanciate_pattern/unfold_cont/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
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<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p11" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p12"/>
<org.eventb.core.prHypAction name="REWRITE6" org.eventb.core.prHidden="p13" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p14"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="⊤"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="unfold_root_c/unfold_cont/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
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<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38,p39">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="Pattern⊆Model"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
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<org.eventb.core.prPred name="p42" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒todo(c)=((to_unfold_c∩{c})∪to_unfold_c_in[{c}]) × (containers∼[{c}] → 0 ‥ max(ran(c_multiplicity)))">
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
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<org.eventb.core.prPred name="p43" org.eventb.core.predicate="todo∈components[{Pat}] → (Component ↔ (components[{Pat}] ⇸ ℕ))">
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</org.eventb.core.prPred>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="∀m⦂Model·containers[components[{m}]]⊆components[{m}]"/>
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="dom(inst_components) ◁ containers;inst_components⊆inst_components;containers"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p43">
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
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<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p48" org.eventb.core.predicate="{s⦂Component·s∈container∼[{c}] ∖ c_multiplicity∼[{0}] ∣ s ↦ (to_unfold_c_in[{s}]∪ran(new_c)) × weight(s)}(c0)=((to_unfold_c∩{c0})∪((to_unfold_c_in ∖ {c ↦ dest})∪((container∼[{c}] ∖ c_multiplicity∼[{0}]) × ran(new_c)))[{c0}]) × weight(c0)">
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<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(Component×ℙ(Component×ℤ)))"/>
<org.eventb.core.prIdent name="weight" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(λc⦂Component·c∈components[{Pat}] ∣ containers∼[{c}] ∖ components[{Inst}] → 0 ‥ max(ran(c_mult)))∈({Inst} ⩤ components)[{Pat}] → ℙ(({Inst} ⩤ components)[{Pat}] ⇸ ℕ)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="(λc⦂Component·c∈components[{Pat}] ∣ containers∼[{c}] ∖ components[{Inst}] → 0 ‥ max(ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})))∈({Inst} ⩤ components)[{Pat}] ⇸ ℙ(({Inst} ⩤ components)[{Pat}] ⇸ ℕ)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="inst_components∼∈components[{Mdl}] ⇸ components[{Pat}]"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒¬c_mult=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult)⇒b≥x)"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="(λc⦂Component·c∈components[{Pat}] ∣ containers∼[{c}] ∖ components[{Inst}] → 0 ‥ max(ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})))∈({Inst} ⩤ components)[{Pat}] → ℙ(({Inst} ⩤ components)[{Pat}] ⇸ ℕ)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒(¬c_mult_others=(∅ ⦂ ℙ(Component×ℤ))∨(∃pc⦂Component·¬¬pc∈dom(inst_components)))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})⇒b≥x)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="weight∈components[{Pat}] → ℙ(components[{Pat}] ⇸ ℕ)"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="∀pc⦂Component·pc∈dom(inst_components)⇒finite(inst_components[{pc}])"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p56" org.eventb.core.predicate="dom(λc⦂Component·c∈components[{Pat}] ∣ containers∼[{c}] ∖ components[{Inst}] → 0 ‥ max(ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})))=({Inst} ⩤ components)[{Pat}]"/>
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<org.eventb.core.prPred name="p49" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒weight(c)=containers∼[{c}] → 0 ‥ max(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒(¬c_mult_others=(∅ ⦂ ℙ(Component×ℤ))∨¬(∀pc⦂Component·¬pc∈dom(inst_components)))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})⇒b≥x)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="container⊆containers"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prPred name="p57" org.eventb.core.predicate="components[{Pat}]=({Inst} ⩤ components)[{Pat}]"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒¬c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})⇒b≥x)"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒(¬c_mult_others=(∅ ⦂ ℙ(Component×ℤ))∨(∃pc⦂Component·pc∈dom(inst_components)))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})⇒b≥x)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="todo∈components[{Pat}] → (Component ↔ (components[{Pat}] ⇸ ℕ))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="inst_components∈components[{Pat}] ↔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒ran(c_mult)≠(∅ ⦂ ℙ(ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult)⇒b≥x)"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="c_mult=c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="c_mult_others∈components[{Pat}] ∖ dom(inst_components) → ℕ"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒¬(c_mult_others=(∅ ⦂ ℙ(Component×ℤ))∧(∀pc⦂Component·¬pc∈dom(inst_components)))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])})⇒b≥x)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒todo(c)=((to_unfold_c∩{c})∪to_unfold_c_in[{c}]) × weight(c)"/>
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<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.rmL1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
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<org.eventb.core.lang name="L"/>
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<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p9"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_mult_others" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="weight" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Pat∈Pattern">
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="containers∼[{c}] ∖ components[{Inst}] → 0 ‥ max(ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}))=(containers ∖ (components[{Inst}] × components[{Inst}]))∼[{c}] → 0 ‥ max(ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="weight∈components[{Pat}] → ℙ(components[{Pat}] ⇸ ℕ)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)">
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="c∈({Inst} ⩤ components)[{Pat}]">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="containers∼[{c}] ∖ components[{Inst}] → 0 ‥ max(ran(c_mult))=(containers ∖ (components[{Inst}] × components[{Inst}]))∼[{c}] → 0 ‥ max(ran(c_mult))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))">
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒weight(c)=containers∼[{c}] → 0 ‥ M"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="∀pc⦂Component·pc∈dom(inst_components)⇒finite(inst_components[{pc}])"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))">
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="Mdl∈Model ∖ Pattern">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="inst_components∈components[{Pat}] ↔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="c∈components[{Pat}]⇒¬c_mult=(∅ ⦂ ℙ(Component×ℤ))∧(∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_mult)⇒b≥x)">
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<org.eventb.core.prPred name="p28" org.eventb.core.predicate="c_mult_others∈components[{Pat}] ∖ dom(inst_components) → ℕ"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="¬c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
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<org.eventb.core.prPred name="p39" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
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<org.eventb.core.prPred name="p42" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]⇒todo(c)=((to_unfold_c∩{c})∪to_unfold_c_in[{c}]) × weight(c)"/>
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<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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<org.eventb.core.prPred name="p17" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
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<org.eventb.core.prPred name="p40" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="¬Inst=Mdl"/>
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<org.eventb.core.prPred name="p33" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
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<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p83" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧¬m∈ran(c_indexes)∧s∈dom(e)⇒¬e∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
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<org.eventb.core.prPred name="p81" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧¬(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈ran(c_indexes)⇒¬m∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p85" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p79" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
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<org.eventb.core.prPred name="p32" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
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<org.eventb.core.prPred name="p65" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p90" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p73" org.eventb.core.predicate="todo∈components[{Pat}] → ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="inst_components∈components[{Pat}] ↔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p78" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="¬(c_mult_others=(∅ ⦂ ℙ(Component×ℤ))∧(∀pc⦂Component·¬pc∈dom(inst_components)))"/>
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<org.eventb.core.prPred name="p40" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="c_mult=c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="c_mult_others∈components[{Pat}] ∖ dom(inst_components) → ℕ"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p56" org.eventb.core.predicate="¬c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p80" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∉ran(c_indexes)⇒m∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p82" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧m∉ran(c_indexes)∧s∈dom(e)⇒e∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="M_fin/THM" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35" org.eventb.core.prSets="Component,Model" org.eventb.core.psManual="true">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p39">
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<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p40">
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<org.eventb.core.prAnte name="'">
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<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p40" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36">
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<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p41">
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<org.eventb.core.prExprRef name=".expr" org.eventb.core.prRef="e1"/>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] ⇸ ℕ"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
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<org.eventb.core.prPred name="p24" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
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<org.eventb.core.prPred name="p41" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prExpr name="e1" org.eventb.core.expression="components[{Pat}] ⇸ ℕ"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.finiteFunRan"/>
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<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
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<org.eventb.core.prProof name="P_fin/THM" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36,p37,p38,p39" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="m∈((containers ▷ P)∪(id ⦂ ℙ(Component×Component)))[{c}] → 1 ‥ max(ran(c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}))">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="c∈P∧m∈((containers ▷ P)∪(id ⦂ ℙ(Component×Component)))[{c}] → 1 ‥ max(ran(c_mult))⇒dom(m)⊆(P ◁ containers ▷ P)[{c}]∪{c}">
<org.eventb.core.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="components∈Model ↔ Component">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i)∪{c ↦ k}∈todo(c)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈P∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}"/>
<org.eventb.core.prPred name="p61" org.eventb.core.predicate="dom(m)⊆(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}]))[{c0}]∪{c0}">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p68" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈components[{Pat}]∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒c_indexes(i)=inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index)"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="m∈(todo{c ↦ todo(c) ∖ {k⦂ℤ·k∈1 ‥ max(ran(c_multiplicity)) ∣ c_indexes(dest){c ↦ k}}})(c0)">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p41" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="todo∈components[{Pat}] → ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="c0∈P">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p60" org.eventb.core.predicate="m∈(todo{c ↦ todo(c) ∖ {k⦂ℤ·k∈1 ‥ M ∣ c_indexes(dest){c ↦ k}}})(c0)">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p42" org.eventb.core.predicate="P=components[{Pat}]"/>
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<org.eventb.core.prPred name="p44" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p46" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="finite(components[{Pat}])"/>
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<org.eventb.core.prPred name="p51" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
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<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
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<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p60" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (components[{Pat}] ⇸ 1 ‥ M)"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
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<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="components[{Pat}]=(components∪({Mdl} × ran(new_components)))[{Pat}]"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
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<org.eventb.core.prPred name="p34" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
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<org.eventb.core.prPred name="p39" org.eventb.core.predicate="containers;containers⊆containers"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.lang name="L"/>
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p5" org.eventb.core.prHyps=""/>
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<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂Component,i⦂Component·i ↦ c∈(∅ ⦂ ℙ(Component×Component))⇒((∅ ⦂ ℙ(Component×Component))∼;(((containers ∖ (components[{Inst}] × components[{Inst}]))∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ (∅ ⦂ ℙ(Component×ℤ))))({c} × 1 ‥ max(ran(c_mult)))⊆(λc⦂Component·c∈P ∣ (containers[{c}]∪{c}) × 1 ‥ max(ran(c_mult)))(c)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
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<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="i ↦ c∈inst2pat_c∪(ran(new_c) × {c})">
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="∀c⦂Component,i⦂Component·i ↦ c∈inst2pat_c⇒(inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index))({c} × 1 ‥ M)⊆todo(c)"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="todo∈components[{Pat}] → (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]">
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<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.inclusionSetMinusRightRewrites"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r9" org.eventb.core.prRID="org.eventb.core.seqprover.funImgSimplifies:0"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p146" org.eventb.core.predicate="c_indexes(x0)=({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(x1)}">
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<org.eventb.core.prPred name="p155" org.eventb.core.predicate="∃x⦂Component·c ↦ x∈inst2pat_c∼∧x ↦ new_c∼(x1)∈(containers∪(id ⦂ ℙ(Component×Component)))[{x0}] ◁ c_index">
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<org.eventb.core.prPred name="p135" org.eventb.core.predicate="x0∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)∧dest∈dom(c_indexes)∧x1∈ran(new_c)∧new_c∼∈Component ⇸ ℤ">
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<org.eventb.core.prPred name="p171" org.eventb.core.predicate="x2∈containers[{x0}]∨x2∈{x0}">
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<org.eventb.core.prPred name="p79" org.eventb.core.predicate="x∈(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]">
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<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p53" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p174" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo">
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p181" org.eventb.core.predicate="i∈dom(new_c∼)">
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<org.eventb.core.prPred name="p145" org.eventb.core.predicate="c∈containers[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]∪(ran(new_c) × {dest})[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]∪(ran(new_c) × containers[{dest}])[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]∪{(inst2pat_c∪(ran(new_c) × {c}))(i)}">
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<org.eventb.core.prPred name="p143" org.eventb.core.predicate="x ↦ x0∈{c} ⩤ c_indexes(dest)∨(⊤∧⊤)">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p93" org.eventb.core.predicate="(∀i⦂Component·i∈ran(new_c)⇒dest∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)∧i∈ran(new_c)∧new_c∼∈Component ⇸ ℤ)∧i∈ran(new_c)∧{i⦂Component·i∈ran(new_c) ∣ i ↦ ({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}}∈Component ⇸ ℙ(Component × ℤ)">
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<org.eventb.core.prPred name="p125" org.eventb.core.predicate="x∈(ran(new_c) × {dest})[{c}]∨x∈(ran(new_c) × containers[{dest}])[{c}]∨x=c">
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<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c∪(ran(new_c) × {c}))⇒dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈P∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p123" org.eventb.core.predicate="(inst2pat_c∪(ran(new_c) × {c}))(i)=c">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p169" org.eventb.core.predicate="∀m⦂ℙ(Component×ℤ),p⦂Component·m∈todo∧p∈dom(m)⇒containers[{p}]⊆dom(m)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p171" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈components[{Pat}]∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p90" org.eventb.core.predicate="¬i∈dom(inst2pat_c)">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p29" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p94" org.eventb.core.predicate="(∀i⦂Component·i∈ran(new_c)⇒dest∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)∧i∈ran(new_c)∧new_c∼∈Component ⇸ ℤ)∧⊤∧{i⦂Component·i∈ran(new_c) ∣ i ↦ ({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}}∈Component ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p67" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p106" org.eventb.core.predicate="x ↦ x0∈{i⦂Component·i∈ran(new_c) ∣ i ↦ ({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}}(i)">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p167" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p127" org.eventb.core.predicate="x∈(ran(new_c) × {dest})[{c}]∨x∈(ran(new_c) × containers[{dest}])[{c}]">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p170" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ M)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p131" org.eventb.core.predicate="¬x∈(ran(new_c) × containers[{dest}])[{c}]">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p73" org.eventb.core.predicate="todo∈components[{Pat}] → ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p194" org.eventb.core.predicate="c∈dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))">
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<org.eventb.core.prPred name="p155" org.eventb.core.predicate="containers[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]⊆dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))∧(ran(new_c) × {dest})[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]⊆dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))∧(ran(new_c) × containers[{dest}])[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]⊆dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))∧(inst2pat_c∪(ran(new_c) × {c}))(i)∈dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))">
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<org.eventb.core.prPred name="p153" org.eventb.core.predicate="¬i=c">
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<org.eventb.core.prPred name="p47" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="finite(components[{Pat}])"/>
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<org.eventb.core.prPred name="p50" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
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<org.eventb.core.prPred name="p180" org.eventb.core.predicate="∀i⦂Component·i∈ran(new_c)⇒i∈dom(new_c∼)"/>
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<org.eventb.core.prPred name="p116" org.eventb.core.predicate="x∈containers[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]∨x∈(ran(new_c) × {dest})[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]∨x∈(ran(new_c) × containers[{dest}])[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]∨x=(inst2pat_c∪(ran(new_c) × {c}))(i)">
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<org.eventb.core.prPred name="p101" org.eventb.core.predicate="c_indexes∈Component ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p130" org.eventb.core.predicate="¬x∈(ran(new_c) × {dest})[{c}]">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p146" org.eventb.core.predicate="c ↦ new_c∼(i)∈(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ ({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}})(i)">
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<org.eventb.core.prPred name="p92" org.eventb.core.predicate="(∀i⦂Component·i∈ran(new_c)⇒dest∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)∧i∈dom(new_c∼)∧new_c∼∈Component ⇸ ℤ)∧i∈dom({i⦂Component·i∈ran(new_c) ∣ i ↦ ({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}})∧{i⦂Component·i∈ran(new_c) ∣ i ↦ ({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}}∈Component ⇸ ℙ(Component × ℤ)">
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<org.eventb.core.prPred name="p11" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p177" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p57" org.eventb.core.predicate="i∈dom(inst2pat_c∪(ran(new_c) × {c}))⇒dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))=(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]">
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p135" org.eventb.core.predicate="inst2pat_c∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p103" org.eventb.core.predicate="{i⦂Component·i∈ran(new_c) ∣ i ↦ ({c} ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}}∈Component ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p141" org.eventb.core.predicate="x0=new_c∼(i)">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_multiplicity∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p151" org.eventb.core.predicate="c∈ran(new_c)"/>
<org.eventb.core.prPred name="p164" org.eventb.core.predicate="i∈dom(c_indexes)∪dom({i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p22" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))⊆(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p64" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ M)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
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<org.eventb.core.prPred name="p26" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p191" org.eventb.core.predicate="(ran(new_c) × {dest})[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]⊆dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p27" org.eventb.core.predicate="card(ran(new_c))=c_multiplicity(c)"/>
<org.eventb.core.prPred name="p163" org.eventb.core.predicate="i∈dom(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})">
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<org.eventb.core.prPred name="p72" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p122" org.eventb.core.predicate="inst2pat_c∪(ran(new_c) × {c})∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p188" org.eventb.core.predicate="containers[{c}]⊆((containers∪(id ⦂ ℙ(Component×Component)))[{inst2pat_c(dest)}] ∖ {c})∪{c}"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p74" org.eventb.core.predicate="dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ (dom({c ↦ new_c∼(i)}) ⩤ c_indexes(dest))∪{c ↦ new_c∼(i)}})(i))⊆(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p121" org.eventb.core.predicate="⊤∧inst2pat_c∪(ran(new_c) × {c})∈Component ⇸ Component"/>
<org.eventb.core.prPred name="p166" org.eventb.core.predicate="c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}∈Component ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p98" org.eventb.core.predicate="i0∈ran(new_c)">
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<org.eventb.core.prPred name="p176" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
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<org.eventb.core.prPred name="p42" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
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<org.eventb.core.prPred name="p118" org.eventb.core.predicate="¬x∈containers[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]">
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
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<org.eventb.core.prPred name="p30" org.eventb.core.predicate="container⊆containers"/>
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<org.eventb.core.prPred name="p158" org.eventb.core.predicate="containers[{c}]⊆dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))">
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<org.eventb.core.prPred name="p89" org.eventb.core.predicate="¬i∈dom(c_indexes)">
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<org.eventb.core.prPred name="p140" org.eventb.core.predicate="c ↦ inst2pat_c(dest)∈container"/>
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<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p148" org.eventb.core.predicate="(containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])∪(id ⦂ ℙ(Component×Component)))[{(inst2pat_c∪(ran(new_c) × {c}))(i)}]⊆dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i))">
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<org.eventb.core.prPred name="p50" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p146" org.eventb.core.predicate="∀i⦂Component·i∈ran(new_c)⇒⊤∧i∈ran(new_c)∧⊤"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p136" org.eventb.core.predicate="i1∈dom(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})∧dest∈dom(c_indexes)∧new_c∼∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p153" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧m∉ran(c_indexes)∧s∈dom(e)⇒e∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p61" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
<org.eventb.core.prIdent name="b" org.eventb.core.type="ℤ"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p127" org.eventb.core.predicate="x0=x1">
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="new_c∈1 ‥ c_multiplicity(c) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p92" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i2)⊆dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i2)) ◁ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(c)">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="i1 ↦ i2∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p133" org.eventb.core.predicate="(∀i⦂Component·i∈ran(new_c)⇒i∈dom(new_c∼))∧i1∈dom(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})∧⊤∧dest∈dom(c_indexes)∧⊤∧i1∈dom(new_c∼)∧new_c∼∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p80" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (components[{Pat}] ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p102" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p159" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒¬{c ↦ k}∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p85" org.eventb.core.predicate="i1 ↦ c∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p122" org.eventb.core.predicate="c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}∈Component ↔ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p149" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p94" org.eventb.core.predicate="i1∈ran(new_c)">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p132" org.eventb.core.predicate="(∀i⦂Component·i∈ran(new_c)⇒i∈dom(new_c∼))∧i1∈dom(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})∧c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}∈Component ⇸ ℙ(Component × ℤ)∧dest∈dom(c_indexes)∧c_indexes∈Component ⇸ ℙ(Component × ℤ)∧i1∈dom(new_c∼)∧new_c∼∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p59" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p103" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,s⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧s ↦ c∈containers∪(id ⦂ ℙ(Component×Component))∧m∈ran(c_indexes)⇒s∉dom(m)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p87" org.eventb.core.predicate="¬i2=c">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p107" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p169" org.eventb.core.predicate="i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p125" org.eventb.core.predicate="x ↦ x0∈c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p137" org.eventb.core.predicate="i1∈dom(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p89" org.eventb.core.predicate="¬i2∈ran(new_c)">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
<org.eventb.core.prPred name="p68" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈P∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p129" org.eventb.core.predicate="∀i⦂Component·i∈ran(new_c)⇒dest∈dom(c_indexes)∧i∈dom(new_c∼)∧new_c∼∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p158" org.eventb.core.predicate="∀c⦂Component,s⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧s ↦ c∈containers∪(id ⦂ ℙ(Component×Component))∧m∈ran(c_indexes)⇒¬s∈dom(m)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∃b⦂ℤ·∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="i1∈dom(inst2pat_c∪(ran(new_c) × {c}))">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p172" org.eventb.core.predicate="i1 ↦ i2∈containers">
<org.eventb.core.prIdent name="i1" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p98" org.eventb.core.predicate="∀m⦂ℙ(Component×ℤ),p⦂Component·m∈todo∧p∈dom(m)⇒containers[{p}]⊆dom(m)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c∪(ran(new_c) × {c}))∧i2∈dom(inst2pat_c∪(ran(new_c) × {c}))∧i1 ↦ i2∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])⇒(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i2)=dom((c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i2)) ◁ (c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i1)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p91" org.eventb.core.predicate="c ↦ i2∈containers∪(ran(new_c) × {dest})∪(ran(new_c) × containers[{dest}])">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p73" org.eventb.core.predicate="todo∈P → ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p100" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p130" org.eventb.core.predicate="(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})(i2)=c_indexes(i2)">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="c ↦ dest∈to_unfold_c_in"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p58" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p70" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p76" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈components[{Pat}]∧m∈todo(c)⇒dom(m)⊆containers[{c}]∪{c}">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p154" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧¬m∈ran(c_indexes)∧s∈dom(e)⇒¬e∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p88" org.eventb.core.predicate="i2∈ran(new_c)">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p104" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i)∪{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) → (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p96" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p120" org.eventb.core.predicate="i2∈dom(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p112" org.eventb.core.predicate="(∀i⦂Component·i∈ran(new_c)⇒dest∈dom(c_indexes)∧i∈dom(new_c∼)∧new_c∼∈Component ⇸ ℤ)∧i2∈dom(c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}})∧c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}∈Component ⇸ ℙ(Component × ℤ)∧⊤∧c_indexes∈Component ⇸ ℙ(Component × ℤ)">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p171" org.eventb.core.predicate="i2∈dom(inst2pat_c)">
<org.eventb.core.prIdent name="i2" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p115" org.eventb.core.predicate="i∈ran(new_c)⇒dest∈dom(c_indexes)∧i∈ran(new_c)∧new_c∼∈Component ⇸ ℤ">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p99" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ M)">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p78" org.eventb.core.predicate="todo∈components[{Pat}] → ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(Component×ℙ(ℙ(Component×ℤ)))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p84" org.eventb.core.predicate="c∈dom(inst2pat_c∪(ran(new_c) × {c}))"/>
<org.eventb.core.prPred name="p126" org.eventb.core.predicate="x ↦ x1∈c_indexes∪{i⦂Component·i∈ran(new_c) ∣ i ↦ c_indexes(dest){c ↦ new_c∼(i)}}">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p97" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i)∪{c ↦ k}∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p108" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo">
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p93" org.eventb.core.predicate="¬i1=c">
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<org.eventb.core.prPred name="p83" org.eventb.core.predicate="containers[{i}]=(∅ ⦂ ℙ(Component))">
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<org.eventb.core.prPred name="p203" org.eventb.core.predicate="x1 ↦ x0∈new_c∼">
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<org.eventb.core.prIdent name="x1" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p30" org.eventb.core.predicate="container⊆containers"/>
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<org.eventb.core.prPred name="p201" org.eventb.core.predicate="x ↦ x1∈inst2pat_c∼">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p35" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p142" org.eventb.core.predicate="x1∈{dest}∪containers[{dest}]∪{i}">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p190" org.eventb.core.predicate="c ↦ inst2pat_c(dest)∈container"/>
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<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p170" org.eventb.core.predicate="c ↦ x1∈inst2pat_c∼∨x1∈ran(new_c)">
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<org.eventb.core.prPred name="p193" org.eventb.core.predicate="x1∈dom(inst2pat_c)">
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<org.eventb.core.prPred name="p204" org.eventb.core.predicate="x1 ↦ x0∈c_index∨⊤">
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p42" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p101" org.eventb.core.predicate="x ↦ x1∈inst2pat_c∼∨(x=c∧x1∈ran(new_c))">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p97" org.eventb.core.predicate="x1 ↦ x0∈({dest}∪containers[{dest}]∪{i}) ◁ (c_index∪new_c∼)">
<org.eventb.core.prIdent name="i" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x0" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p166" org.eventb.core.predicate="x ↦ x1∈inst2pat_c∼∨(⊤∧x1∈ran(new_c))">
<org.eventb.core.prIdent name="x" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="x1" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p133" org.eventb.core.predicate="x2 ↦ x4∈c_indexes">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p62" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p71" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂Component·c∈to_unfold_c⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒¬{c ↦ k}∈ran(c_indexes)"/>
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<org.eventb.core.prPred name="p60" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)"/>
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<org.eventb.core.prPred name="p57" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="inst_components∼∈components[{Mdl}] ⇸ components[{Pat}]"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀pc⦂Component·pc∈dom(inst_components)⇒finite(inst_components[{pc}])"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="dest" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p45" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p47" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))"/>
<org.eventb.core.prPred name="p68" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p51" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p52" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p53" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p73" org.eventb.core.predicate="finite(components[{Pat}])"/>
<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p56" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p60" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.smt.core.externalSMT"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
</org.eventb.core.prProof>
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<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p46" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p56"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p57"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p58"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∀ goal (frees m,p)" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p59">
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="p" org.eventb.core.type="Component"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⇒ goal" org.eventb.core.prGoal="p59" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p62" org.eventb.core.prHyps="p60,p61">
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="sl/ds" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p64"/>
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<org.eventb.core.prAnte name="'">
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<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p40" org.eventb.core.prInfHyps="p66"/>
<org.eventb.core.prHypAction name="FORWARD_INF2" org.eventb.core.prHyps="p38" org.eventb.core.prInfHyps="p67"/>
<org.eventb.core.prHypAction name="FORWARD_INF3" org.eventb.core.prHyps="p63" org.eventb.core.prInfHyps="p68"/>
<org.eventb.core.prHypAction name="FORWARD_INF4" org.eventb.core.prHyps="p25" org.eventb.core.prInfHyps="p69"/>
<org.eventb.core.prHypAction name="DESELECT5" org.eventb.core.prHyps="p41,p38,p63,p40,p25"/>
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with P=components[{Pat}]" org.eventb.core.prHyps="p42">
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<org.eventb.core.prHypAction name="FORWARD_INF2" org.eventb.core.prHyps="p66" org.eventb.core.prInfHyps="p72"/>
<org.eventb.core.prHypAction name="FORWARD_INF3" org.eventb.core.prHyps="p69" org.eventb.core.prInfHyps="p73"/>
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<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R1000"/>
<org.eventb.core.prString name=".config_id" org.eventb.core.prSValue="CVC3"/>
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst2pat_c" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="new_components" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="todo" org.eventb.core.type="ℙ(ℙ(Component×ℤ))"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_unfold_c∩dom(to_unfold_c_in)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒dom(c_indexes(i))=(containers∪(id ⦂ ℙ(Component×Component)))[{inst2pat_c(i)}]"/>
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<org.eventb.core.prPred name="p64" org.eventb.core.predicate="∀x⦂ℤ·x∈ran(c_multiplicity)⇒b≥x">
<org.eventb.core.prIdent name="b" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="finite(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="c_multiplicity∈components[{Pat}] → ℕ"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p66" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Pat∈Pattern"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="M=max(ran(c_multiplicity))"/>
<org.eventb.core.prPred name="p56" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))"/>
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<org.eventb.core.prPred name="p67" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ max(ran(c_multiplicity))⇒{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p62" org.eventb.core.predicate="(containers∪(new_components∼;containers;inst_components;containers)∪(new_components∼;containers;(new_components∪inst_components)))[{p}]⊆dom(m)">
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<org.eventb.core.prIdent name="p" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="containers∈ran(components) ↔ ran(components)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="todo∈ℙ(components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
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<org.eventb.core.prPred name="p71" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (components[{Pat}] ⇸ 1 ‥ max(ran(c_multiplicity)))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="containers∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒containers[{i}]⊆dom(inst2pat_c)"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀i1⦂Component,i2⦂Component·i1∈dom(inst2pat_c)∧i2∈dom(inst2pat_c)∧i1 ↦ i2∈containers⇒c_indexes(i2)=dom(c_indexes(i2)) ◁ c_indexes(i1)"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀m⦂ℙ(Component×ℤ),p⦂Component·m∈todo∧p∈dom(m)⇒containers[{p}]⊆dom(m)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="components;containers;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ M∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="¬Inst=Mdl"/>
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<org.eventb.core.prPred name="p27" org.eventb.core.predicate="to_unfold_c_in;inst2pat_c⊆container"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∀i⦂Component·i∈dom(inst2pat_c)⇒c_indexes(i)=inst2pat_c∼;((containers∪(id ⦂ ℙ(Component×Component)))[{i}] ◁ c_index)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="container⊆containers"/>
<org.eventb.core.prPred name="p68" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒c_indexes(i)∪{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="components;containers∼;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀m⦂Model·finite(components[{m}])"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="todo∈ℙ(P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p63" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i)∪{c ↦ k}∈todo"/>
<org.eventb.core.prPred name="p69" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p73" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ)·s∈components[{Pat}]∧c∈components[{Pat}]∧s ↦ c∈containers∧m∈(containers∪(id ⦂ ℙ(Component×Component)))[{s}] → 1 ‥ max(ran(c_multiplicity))∧(containers∪(id ⦂ ℙ(Component×Component)))[{c}] ◁ m∈todo⇒m∈todo"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="P=components[{Pat}]"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p54" org.eventb.core.predicate="c∈dom(c_multiplicity)"/>
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<org.eventb.core.lang name="L"/>
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<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧m∉ran(c_indexes)∧s∈dom(e)⇒e∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component,s⦂Component,m⦂ℙ(Component×ℤ),e⦂ℙ(Component×ℤ)·s∈P∧c∈P∧s ↦ c∈containers∧e∈Component ⇸ 1 ‥ M∧m∈Component ⇸ 1 ‥ M∧dom(m)⊆(containers∪(id ⦂ ℙ(Component×Component)))[{c}]∧¬m∈ran(c_indexes)∧s∈dom(e)⇒¬e∈ran(c_indexes)">
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
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</org.eventb.core.prAnte>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="c_mult" org.eventb.core.type="ℙ(Component×ℤ)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈(components[{Pat}] ∖ dom(container)) ∖ c_mult∼[{0}]∧m∈ran(∅ ⦂ ℙ(Component×ℙ(Component×ℤ)))⇒c∉dom(m)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p58" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p59"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p28" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p60"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p42" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p61"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p63"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p64"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∀ goal (frees c0,m)" org.eventb.core.prGoal="p62" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p65">
<org.eventb.core.prIdent name="c0" org.eventb.core.type="Component"/>
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<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⇒ goal" org.eventb.core.prGoal="p65" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p68" org.eventb.core.prHyps="p66,p67">
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<org.eventb.core.prIdent name="c_index" org.eventb.core.type="ℙ(Component×ℤ)"/>
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<org.eventb.core.prIdent name="new_c" org.eventb.core.type="ℙ(ℤ×Component)"/>
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
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<org.eventb.core.prIdent name="i0" org.eventb.core.type="Component"/>
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<org.eventb.core.prPred name="p168" org.eventb.core.predicate="∃i⦂Component·i∈ran(new_c)∧c_indexes(dest){c ↦ new_c∼(i)}=m">
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<org.eventb.core.prPred name="p62" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="finite(P)"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="components∼∈Component ⇸ Model"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="∀s⦂Component,c⦂Component·s ↦ c∈container⇒containers∼[{s}]⊂containers∼[{c}]"/>
<org.eventb.core.prPred name="p65" org.eventb.core.predicate="containers⊆container;(containers∪(id ⦂ ℙ(Component×Component)))"/>
<org.eventb.core.prPred name="p72" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ max(ran(c_multiplicity))⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="c_index∈dom(inst2pat_c) → ℕ"/>
<org.eventb.core.prPred name="p39" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="c_indexes∈dom(inst2pat_c) ↣ (P ⇸ 1 ‥ M)"/>
<org.eventb.core.prPred name="p41" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)"/>
<org.eventb.core.prPred name="p42" org.eventb.core.predicate="P=components[{Pat}]"/>
<org.eventb.core.prPred name="p43" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p44" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p45" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p47" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p48" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p49" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p50" org.eventb.core.predicate="containers;containers⊆containers"/>
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<org.eventb.core.prPred name="p52" org.eventb.core.predicate="ran(new_components)∩ran(container)=(∅ ⦂ ℙ(Component))"/>
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<org.eventb.core.prPred name="p54" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p55" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p64" org.eventb.core.predicate="components∈Model ↔ Component"/>
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<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p6" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p7"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p8" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p9"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p10" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p11"/>
<org.eventb.core.prHypAction name="REWRITE6" org.eventb.core.prHidden="p12" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p13"/>
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<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="0.0"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂Component,i⦂Component,m⦂ℙ(Component×ℤ)·c ↦ i∈to_unfold_c_in∧c_indexes(i)⊆m∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒¬c∈dom(m)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p4" org.eventb.core.predicate="ran(c_multiplicity)≠(∅ ⦂ ℙ(ℤ))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒¬c_indexes(i){c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬P=(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="dom(inst_components) ◁ (container;inst_components)⊆inst_components;container">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂Component,m⦂ℙ(Component×ℤ)·c∈to_unfold_c∧m∈ran(c_indexes)⇒c∉dom(m)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒¬{c ↦ k}∈ran(c_indexes)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="¬c_multiplicity=(∅ ⦂ ℙ(Component×ℤ))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="P≠(∅ ⦂ ℙ(Component))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="P" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂Component,k⦂ℤ·c∈to_unfold_c∧k∈1 ‥ M⇒{c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="components∈Model ↔ Component">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.domCompRewrites"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="Pattern⊆Model">
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<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂Component,i⦂Component,k⦂ℤ·c ↦ i∈to_unfold_c_in∧k∈1 ‥ M⇒c_indexes(i){c ↦ k}∉ran(c_indexes)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c_in" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Inst≠Mdl">
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<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prIdent name="c_multiplicity" org.eventb.core.type="ℙ(Component×ℤ)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="M" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="c_indexes" org.eventb.core.type="ℙ(Component×ℙ(Component×ℤ))"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∃C⦂ℙ(Component×Component)·container⊆C∧C;C⊆C">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="Pattern⊆Model">
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Inst≠Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬(∀C⦂ℙ(Component×Component)·¬(container⊆C∧C;C⊆C))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="container⊆C">
<org.eventb.core.prIdent name="C" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="C;C⊆C">
<org.eventb.core.prIdent name="C" org.eventb.core.type="ℙ(Component×Component)"/>
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="{C⦂ℙ(Component×Component)·container⊆C∧C;C⊆C ∣ C}≠(∅ ⦂ ℙ(ℙ(Component×Component)))">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∃C⦂ℙ(Component×Component)·¬¬(container⊆C∧C;C⊆C)">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="container" org.eventb.core.type="ℙ(Component×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="¬Inst=Mdl">
<org.eventb.core.prIdent name="Inst" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Mdl" org.eventb.core.type="Model"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="components∈Model ↔ Component">
<org.eventb.core.prIdent name="Component" org.eventb.core.type="ℙ(Component)"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
<org.eventb.core.prIdent name="components" org.eventb.core.type="ℙ(Model×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.rn"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.exF"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
</org.eventb.core.prFile>