Pattern-Instanciation-On-System-Engineering-Model/Event-B/pseim/mComponent0.bpr

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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)"/>
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="∀pc⦂Component·pc∈components(Pat)⇒Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)∧pc∈dom(c_multiplicity(Pat))∧c_multiplicity(Pat)∈Component ⇸ ℤ∧finite(inst_components[{pc}])"/>
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<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Mdl∈dom(components)"/>
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<org.eventb.core.prIdent name="pc" org.eventb.core.type="Component"/>
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<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="p3" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="¬Mdl=Pat"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="pc∈components(Pat)⇒Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)∧pc∈dom(c_multiplicity(Pat))∧c_multiplicity(Pat)∈Component ⇸ ℤ∧finite(inst_components[{pc}])">
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<org.eventb.core.prPred name="p31" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℕ1"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="pc∈dom(c_multiplicity(Pat))">
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈Model"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂Model·m∈Pattern⇒c_multiplicity(m)∈components(m) → ℕ1"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀pc⦂Component·Pat∈dom(components)∧components∈Model ⇸ ℙ(Component)∧(pc∈components(Pat)⇒Pat∈dom(c_multiplicity)∧c_multiplicity∈Model ⇸ ℙ(Component × ℤ)∧pc∈dom(c_multiplicity(Pat))∧c_multiplicity(Pat)∈Component ⇸ ℤ∧finite(inst_components[{pc}]))"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Mdl≠Pat"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="inst_components∈components(Pat) ↔ components(Mdl)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="Pat∈dom(components)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
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<org.eventb.core.prProof name="instanciate_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,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" org.eventb.core.prSets="Component,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_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="containers" 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.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="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="∀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="∀c⦂Component·c∈dom(to_unfold_c_in)⇒c_multiplicity(c)&gt;0"/>
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<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"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
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<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_mult=c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
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<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="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p40" org.eventb.core.predicate="containers∈Component ↔ Component"/>
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<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∀c⦂Component·finite(containers∼[{c}])"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="containers;containers⊆containers"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀pc⦂Component·pc∈dom(inst_components)⇒finite(inst_components[{pc}])"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
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<org.eventb.core.prPred name="p35" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
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<org.eventb.core.prProof name="instanciate_pattern/to_unfold_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="Pattern" org.eventb.core.type="ℙ(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="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·∃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">
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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)"/>
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</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="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)"/>
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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="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))"/>
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<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="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">
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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="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"/>
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</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">
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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.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)"/>
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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="p12" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<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="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·m1≠m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<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.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.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prProof name="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" 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_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)"/>
<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="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"/>
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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)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="Pat∈dom(components)"/>
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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×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)"/>
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<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="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
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</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">
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</org.eventb.core.prRule>
<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(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)"/>
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<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="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)"/>
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<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.prProof>
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<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="CVC3" org.eventb.core.prGoal="p29" org.eventb.core.prHyps="p12,p11,p3,p1,p2,p4,p5,p6,p7,p8,p9,p28,p10,p13,p14,p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p26,p27">
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</org.eventb.core.prRule>
<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(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="p0" org.eventb.core.predicate="to_clone_c∪(ran(new_c) × {c})∈(components{Pat ↦ components(Pat)∪ran(new_c)})(Pat) ⇸ (components{Pat ↦ components(Pat)∪ran(new_c)})(Pat)"/>
<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="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))"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="c∈to_unfold_c"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<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"/>
<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="p16" org.eventb.core.predicate="dom(to_clone_c)∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<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)"/>
<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="components{Pat ↦ components(Pat)∪ran(new_c)}∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<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="p26" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Pat∈dom(components)"/>
<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>
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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="p15,p1,p17,p11,p3,p13,p19,p12,p16,p9,p2,p5,p20,p21,p14,p4,p18,p6,p10,p7,p8">
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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" 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="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))"/>
<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="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(container)∧container∈Model ⇸ ℙ(Component × Component)∧c∈dom(to_clone_c)∧to_clone_c∈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="c∈dom(to_clone_c)"/>
<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="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="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.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="SELECT0" org.eventb.core.prHyps="p18,p12,p14,p13,p17,p10,p2,p5,p22,p23,p15,p4,p19,p6,p11,p7,p8,p24,p20,p1,p25"/>
<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="p3,p16,p9,p18,p12,p14,p13,p17,p10,p2,p5,p22,p23,p15,p4,p19,p6,p11,p7,p8,p24,p20,p1,p25">
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</org.eventb.core.prRule>
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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)"/>
<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)"/>
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<org.eventb.core.prPred name="p3" 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))"/>
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<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="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"/>
<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="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)"/>
<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.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>
<org.eventb.core.prProof name="clone_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,p21,p22,p23" org.eventb.core.prSets="Component,Model">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p28" org.eventb.core.prHyps="p27">
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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="p26" org.eventb.core.predicate="(container{Pat ↦ container(Pat)∪(ran(cloned_c) × {c})})(m)∈(components{Pat ↦ components(Pat)∪ran(cloned_c)})(m) ⇸ (components{Pat ↦ components(Pat)∪ran(cloned_c)})(m)">
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<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c⊆components(Pat)"/>
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<org.eventb.core.prIdent name="cloned_c" org.eventb.core.type="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.prIdent name="m" org.eventb.core.type="Model"/>
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<org.eventb.core.lang name="L"/>
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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"/>
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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="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.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)"/>
<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)"/>
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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))"/>
<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"/>
<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="p29" org.eventb.core.predicate="to_unfold_c∩to_free_c=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<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="container∈Model → (Component ⇸ Component)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="components{Pat ↦ components(Pat)∪ran(cloned_c)}∈Model ⇸ ℙ(Component)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c∈dom(to_clone_c)"/>
<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="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.prPred name="p42" org.eventb.core.predicate="¬m=Pat">
<org.eventb.core.prIdent name="m" org.eventb.core.type="Model"/>
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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))"/>
<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"/>
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<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">
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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,p17,p3,p1,p18,p12,p4,p14,p20,p13,p16,p2,p6,p21,p22,p15,p5,p19,p7,p11,p8,p9">
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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="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="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"/>
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<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"/>
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<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>
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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_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"/>
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<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)"/>
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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="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">
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<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)"/>
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<org.eventb.core.prPred name="p13" 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="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"/>
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</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>
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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="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="p11" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
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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.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))"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)"/>
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<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))"/>
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
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<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p10" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p11"/>
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<org.eventb.core.prPred name="p46" org.eventb.core.predicate="({Pat} ⩤ container)(m)∈components(Pat)∪ran(new_c) ⇸ ({Pat} ⩤ components)(m)">
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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="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)"/>
</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.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)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="to_free_c⊆components(Pat)"/>
<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="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)"/>
</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="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"/>
<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_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">
<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,p9,p2,p11,p12,p13,p14,p15,p26,p16,p17,p4,p18,p19,p5,p20,p6,p7,p8,p21,p22,p23,p24,p25"/>
<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="p0" org.eventb.core.predicate="Pat∈dom(components)∧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="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="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="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"/>
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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="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>
<org.eventb.core.prProof name="unfold_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.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="p11">
<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"/>
<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.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬(∀sc·¬([[1]]∈sc∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[sc]⊆sc))" 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="p12"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p12"/>
<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="p8" 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="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="remove ¬ in ¬¬([[1]]∈[[0]]∧(({c} ⩤ container(Pat))∪((ran(new_c) × {c});container(Pat)))∼[[[0]]]⊆[[0]])" 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="p14"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p14"/>
<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="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="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="p16"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p17"/>
</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="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="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="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="'">
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<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"/>
<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="p8" org.eventb.core.prHyps="p4" org.eventb.core.prInfHyps="p37"/>
<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="p37" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p38"/>
</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.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="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.prString name=".pos" org.eventb.core.prSValue=""/>
</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=""/>
</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(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="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="p40" org.eventb.core.predicate="c0∈ran(to_clone_c)⇒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="p21" org.eventb.core.predicate="∀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">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<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="p43" org.eventb.core.predicate="∀c⦂Component·c∈dom(to_unfold_c_in)⇒1 ‥ card(to_unfold_c_in[{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="p47" org.eventb.core.predicate="i ↦ c0∈sc∧s ↦ c0∈container⇒1 ‥ i∗c_multiplicity(s) × {s}⊆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="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="p26" org.eventb.core.predicate="sc0⊆ℕ × components[{Pat}]">
<org.eventb.core.prIdent name="sc0" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀c0⦂Component·c0∈ran({c} ⩤ to_clone_c)⇒1 ‥ card(to_clone_c∼[{c0}] ∖ {c}) × {c0}⊆sc">
<org.eventb.core.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" 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="p31" org.eventb.core.predicate="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.prIdent name="sc" org.eventb.core.type="ℙ(ℤ×Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p46" org.eventb.core.predicate="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="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" 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="p6" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p7"/>
<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="p8"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p9"/>
<org.eventb.core.prHypAction name="HIDE2" org.eventb.core.prHyps="p10"/>
<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="p5,p3,p4,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="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="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="p1" org.eventb.core.predicate="container[dom(inst_components)]⊆dom(inst_components)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="containers∈Component ↔ Component">
<org.eventb.core.prIdent name="containers" org.eventb.core.type="ℙ(Component×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="p6" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="dom(inst_components) ◁ container;inst_components⊆inst_components;container"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="inst_components∈components[{Inst}] ⤔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="new_components∈components[{Inst}] ∖ dom(inst_components) ↣ Component ∖ ran(components)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="to_unfold_c⊆components[{Pat}]"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="to_unfold_c⊆(components∪({Mdl} × ran(new_components)))[{Pat}]"/>
<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/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"/>
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<org.eventb.core.prExpr name="e2" org.eventb.core.expression="{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
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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="p27" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="¬Inst=Mdl"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="components∈Model ↔ Component"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="pc∈dom(inst_components)⇒finite(inst_components[{pc}])">
<org.eventb.core.prIdent name="pc" org.eventb.core.type="Component"/>
</org.eventb.core.prPred>
<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="r4" 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.prProof>
<org.eventb.core.prProof name="to_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,p25,p26,p27,p28,p29,p30" 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="p27,p3,p11,p29,p20"/>
<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,p29,p30">
<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="height" org.eventb.core.type="ℙ(Component×ℤ)"/>
<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.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="p3" org.eventb.core.predicate="Pattern⊆Model"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}]∩ran(container)⇒height(c)=1+max(height[container∼[{c}]])"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="container∈ran(components) ⇸ ran(components)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="height∈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="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="Pat∈Pattern"/>
<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"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="dom(to_unfold_c_in)⊆dom(container)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="to_unfold_c∩dom(container)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀c⦂Component·c∈components[{Pat}] ∖ ran(container)⇒height(c)=0"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="ran(to_unfold_c_in)⊆dom(inst2pat_c)"/>
<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="components;container;components∼⊆(id ⦂ ℙ(Model×Model))"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="Inst≠Mdl"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="to_unfold_c∩ran(inst2pat_c)=(∅ ⦂ ℙ(Component))"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="to_unfold_c_in∈components[{Pat}] ↔ components[{Inst}]"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="inst2pat_c;container=container;inst2pat_c"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="(inst2pat_c;to_unfold_c_in)∩container=(∅ ⦂ ℙ(Component×Component))"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀c⦂Component·finite(to_unfold_c_in[{c}])"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∀c⦂Component·finite(container∼[{c}])"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="Mdl∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p30" 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"/>
</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">
<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="p3">
<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="⊤ goal" org.eventb.core.prGoal="p3" org.eventb.core.prHyps=""/>
</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="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="p3" org.eventb.core.predicate="⊤"/>
<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="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.prIdent name="Model" org.eventb.core.type="ℙ(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.prProof>
<org.eventb.core.prProof name="unfold_c/c_index_ty/INV" 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.lang name="L"/>
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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">
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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="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="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.prPred name="p5" 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="components∈Model → ℙ(Component)"/>
<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="c_index∪new_c∼∈dom(to_clone_c∪(ran(new_c) × {c})) ⇸ ℕ"/>
<org.eventb.core.prPred name="p7" 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="p24" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
<org.eventb.core.prPred name="p9" 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="p12" 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="p14" org.eventb.core.predicate="c_multiplicity∈Pattern → (Component ⇸ ℕ)">
<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="to_clone_c∈components(Pat) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="c_multiplicity(Pat)∈Component ⇸ ℤ"/>
<org.eventb.core.prPred name="p15" 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.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))"/>
<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_free_c" org.eventb.core.type="ℙ(Component)"/>
</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>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="c_multiplicity∈Model ⇸ ℙ(Component × ℤ)"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="Pat∈dom(c_multiplicity)"/>
<org.eventb.core.prPred name="p6" 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="p4" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ"/>
<org.eventb.core.prPred name="p10" 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)">
<org.eventb.core.prIdent name="to_unfold_c" org.eventb.core.type="ℙ(Component)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" 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_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,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,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)"/>
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<org.eventb.core.prIdent name="Pat" org.eventb.core.type="Model"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(Component×Component))∈({Inst} ⩤ components)[{Inst}] ⇸ ({Inst} ⩤ components)[{Pat}]"/>
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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"/>
<org.eventb.core.prIdent name="Model" org.eventb.core.type="ℙ(Model)"/>
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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="PP (trivial)" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
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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="to_free_c" org.eventb.core.type="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="p10" 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.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.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="p19" 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="p15" org.eventb.core.predicate="to_clone_c∈components(Pat) ⇸ 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_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="Model" org.eventb.core.type="ℙ(Model)"/>
<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.prIdent name="components" org.eventb.core.type="ℙ(Model×ℙ(Component))"/>
</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="Model" org.eventb.core.type="ℙ(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(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="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))">
<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="p14" org.eventb.core.predicate="components∈Model ⇸ 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="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)"/>
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<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)"/>
</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.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="">
<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,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>
</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"/>
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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"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c∈dom(c_multiplicity(Pat))"/>
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<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">
<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,p17,p10,p3,p6,p22,p23,p15,p5,p19,p8,p11,p24,p21,p2"/>
<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>
</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="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))"/>
<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="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))"/>
<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_to_clone_disjoint/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2" 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="fun. singleton img. in goal" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="hyp" org.eventb.core.prGoal="p2" org.eventb.core.prHyps="p2"/>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p1">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="hyp" org.eventb.core.prGoal="p1" org.eventb.core.prHyps="p1"/>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p4">
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p4" org.eventb.core.prHyps="">
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="*" org.eventb.core.prGoal="p10">
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</org.eventb.core.prRule>
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<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p11">
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<org.eventb.core.prString name=".pos" org.eventb.core.prSValue="0.1.1"/>
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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="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="">
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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="">
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<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="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">
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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="p25" org.eventb.core.predicate="Pat∈dom(components)"/>
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<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)"/>
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<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="container∈Model ⇸ ℙ(Component × 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.prPred name="p25" org.eventb.core.predicate="Pat∈dom(container)"/>
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</org.eventb.core.prProof>
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<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))"/>
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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.prIdent name="c" org.eventb.core.type="Component"/>
<org.eventb.core.prIdent name="to_unfold_c" 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="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>
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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.lang name="L"/>
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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="">
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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="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="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)"/>
<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="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="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="p2,p18,p3,p1,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p19,p20,p21,p22,p23">
<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)"/>
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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"/>
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀m⦂Model·finite(components(m))"/>
<org.eventb.core.prPred name="p16" 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="p18" org.eventb.core.predicate="c∈to_free_c ∖ ran(to_clone_c)"/>
<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="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)"/>
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<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.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="∀c0⦂Component·c0∈dom(c_index)⇒c_index(c0)∈1 ‥ (c_multiplicity{Pat ↦ {c} ⩤ c_multiplicity(Pat)})(Pat)(to_clone_c(c0))"/>
<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))"/>
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<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/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" 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.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="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="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)"/>
<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="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.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="p18,p1,p5,p2,p3,p4,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p19,p20,p21,p22,p23">
<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_mult_others" 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="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="inst_components∼∈components(Mdl) ⇸ components(Pat)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="Pattern⊆Model"/>
<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="p4" org.eventb.core.predicate="components∈Model → ℙ(Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="c_mult_others∈components(Pat) ∖ dom(inst_components) → ℕ"/>
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<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)"/>
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<org.eventb.core.prPred name="p18" org.eventb.core.predicate="inst_components∈components(Pat) ↔ components(Mdl)"/>
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<org.eventb.core.prPred name="p20" 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="p22" org.eventb.core.predicate="Pat∈dom(components)"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="to_unfold_c_in/WD" 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">
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<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="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
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<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="p10">
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</org.eventb.core.prAnte>
<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p11">
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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="Pat" org.eventb.core.type="Model"/>
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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.prIdent name="Pattern" org.eventb.core.type="ℙ(Model)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p2" 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="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="p8" org.eventb.core.predicate="Pat∈Model"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="Inst∈Model"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="Inst∈dom(components)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="components∈Model ⇸ ℙ(Component)"/>
<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="p4" 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="Pat∈dom(components)"/>
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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="r2" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<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="instanciate_pattern/inst_root/WD"/>
<org.eventb.core.prProof name="unfold_c/to_unfold_c_in/INV"/>
<org.eventb.core.prProof name="clone_c/to_unfold_c_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.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×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.prIdent name="container" org.eventb.core.type="ℙ(Model×ℙ(Component×Component))"/>
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<org.eventb.core.prPred name="p11" org.eventb.core.predicate="container∈Model → (Component ⇸ Component)">
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<org.eventb.core.prPred name="p19" org.eventb.core.predicate="c_index∈dom(to_clone_c) ⇸ ℕ">
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<org.eventb.core.prPred name="p3" 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="p22" org.eventb.core.predicate="to_unfold_c⊆components(Pat)">
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(Component×Component))∈({Inst} ⩤ components)[{Pat}] ↔ ({Inst} ⩤ components)[{Inst}]"/>
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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.prProof>
<org.eventb.core.prProof name="instanciate_pattern/pat_root/WD"/>
<org.eventb.core.prProof name="free_c/to_unfold_c_in/INV"/>
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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.prPred name="p9" org.eventb.core.predicate="∀m1⦂Model,m2⦂Model·¬m1=m2⇒components(m1)∩components(m2)=(∅ ⦂ ℙ(Component))"/>
<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.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"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="container∈Model ⇸ ℙ(Component × Component)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="⊤∧⊤∧⊤∧⊤"/>
<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)"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<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"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="instanciate_pattern/cont_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,p27" 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="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.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="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" 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)"/>
<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="Pattern⊆Model"/>
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<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="c_multiplicity∈components[Pattern] → ℕ"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="inst_components∼∈components[{Mdl}] ⇸ components[{Pat}]"/>
<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)"/>
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<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="inst_components∈components[{Pat}] ↔ components[{Mdl}]"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="container∩(id ⦂ ℙ(Component×Component))=(∅ ⦂ ℙ(Component×Component))"/>
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<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="c_mult=c_mult_others{pc⦂Component·pc∈dom(inst_components) ∣ pc ↦ card(inst_components[{pc}])}"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c_mult_others∈components[{Pat}] ∖ dom(inst_components) → 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="p23" org.eventb.core.predicate="∀c⦂Component·c∈dom(inst2pat_c)⇒c_index(c)∈1 ‥ c_multiplicity(inst2pat_c(c))"/>
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<org.eventb.core.prPred name="p25" org.eventb.core.predicate="inst2pat_c∈components[{Inst}] → components[{Pat}]"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="Inst∈Model ∖ Pattern"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="components∈Model ↔ 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="inst_components" org.eventb.core.type="ℙ(Component×Component)"/>
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<org.eventb.core.prPred name="p7" org.eventb.core.predicate="Pattern⊆Model">
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</org.eventb.core.prProof>
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