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bankAccount_M1_accountCreation.bpr
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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<org.eventb.core.prFile version="1">
<org.eventb.core.prProof name="INITIALISATION/invBalance/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="ACCOUNT" 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="PP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="R30000"/>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(ACCOUNT×ℤ))∈ACCOUNT ⇸ ℕ"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="INITIALISATION/invOwner/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1" org.eventb.core.prSets="ACCOUNT,CLIENT">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="K" org.eventb.core.type="ℤ"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(ACCOUNT×CLIENT))∈ACCOUNT ⇸ CLIENT"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="K∈ℕ"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="accountCreation/invBalance/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="ACCOUNT,CLIENT">
<org.eventb.core.lang name="L"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="K" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
<org.eventb.core.prIdent name="balance" org.eventb.core.type="ℙ(ACCOUNT×ℤ)"/>
<org.eventb.core.prIdent name="owner" org.eventb.core.type="ℙ(ACCOUNT×CLIENT)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="a∉dom(balance)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="balance∈ACCOUNT ⇸ ℕ"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="owner∈ACCOUNT ⇸ CLIENT"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬a∈dom(balance)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="a∈ACCOUNT"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="c∈CLIENT">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CLIENT"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="a∉dom(owner)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="K∈ℕ"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬a∈dom(owner)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="balance∪{a ↦ 0}∈ACCOUNT ⇸ ℕ"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="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.prProof>
<org.eventb.core.prProof name="accountCreation/invOwner/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="ACCOUNT,CLIENT">
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<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p5,p2,p3,p6,p7">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="K" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
<org.eventb.core.prIdent name="balance" org.eventb.core.type="ℙ(ACCOUNT×ℤ)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="CLIENT"/>
<org.eventb.core.prIdent name="owner" org.eventb.core.type="ℙ(ACCOUNT×CLIENT)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="a∉dom(balance)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="balance∈ACCOUNT ⇸ ℕ"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="owner∈ACCOUNT ⇸ CLIENT"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬a∈dom(balance)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="a∈ACCOUNT"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="owner∪{a ↦ c}∈ACCOUNT ⇸ CLIENT"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="c∈CLIENT"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="a∉dom(owner)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="K∈ℕ"/>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="accountCreation/balance/EQL" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="ACCOUNT" org.eventb.core.psManual="true">
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3"/>
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<org.eventb.core.prAnte name="'">
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</org.eventb.core.prAnte>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
<org.eventb.core.prIdent name="balance" org.eventb.core.type="ℙ(ACCOUNT×ℤ)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="a∉dom(balance)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="balance∪{a ↦ 0}=balance"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="balance∈ACCOUNT ⇸ ℕ"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="¬a∈dom(balance)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="a∈ACCOUNT"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="c∈CLIENT">
<org.eventb.core.prIdent name="CLIENT" org.eventb.core.type="ℙ(CLIENT)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="CLIENT"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="a∉dom(owner)">
<org.eventb.core.prIdent name="CLIENT" org.eventb.core.type="ℙ(CLIENT)"/>
<org.eventb.core.prIdent name="owner" org.eventb.core.type="ℙ(ACCOUNT×CLIENT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="a ↦ 0∈balance"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬a∈dom(owner)">
<org.eventb.core.prIdent name="CLIENT" org.eventb.core.type="ℙ(CLIENT)"/>
<org.eventb.core.prIdent name="owner" org.eventb.core.type="ℙ(ACCOUNT×CLIENT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
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<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.mngHyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="accountCreation/owner/EQL" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="ACCOUNT,CLIENT" org.eventb.core.psManual="true">
<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="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="CLIENT"/>
<org.eventb.core.prIdent name="owner" org.eventb.core.type="ℙ(ACCOUNT×CLIENT)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="a∉dom(balance)">
<org.eventb.core.prIdent name="balance" org.eventb.core.type="ℙ(ACCOUNT×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬a∈dom(balance)">
<org.eventb.core.prIdent name="balance" org.eventb.core.type="ℙ(ACCOUNT×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="a ↦ c∈owner"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="a∈ACCOUNT"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="c∈CLIENT"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="a∉dom(owner)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="owner∪{a ↦ c}=owner"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="¬a∈dom(owner)"/>
<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="INITIALISATION/invConsistency/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="ACCOUNT,CLIENT">
<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="p1">
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p1" org.eventb.core.prHyps=""/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="dom(∅ ⦂ ℙ(ACCOUNT×ℤ))=dom(∅ ⦂ ℙ(ACCOUNT×CLIENT))"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="accountCreation/invConsistency/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="ACCOUNT,CLIENT">
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀a0⦂ACCOUNT·a0∈dom(balance∪{a ↦ 0})⇒(balance∪{a ↦ 0})(a0)≥0"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="a0∈dom(balance∪{a ↦ 0})⇒(balance∪{a ↦ 0})(a0)≥0">
<org.eventb.core.prIdent name="a0" org.eventb.core.type="ACCOUNT"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="K∈ℕ"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="finite(ACCOUNT)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="¬a∈dom(owner)"/>
<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="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<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.prProof>
<org.eventb.core.prProof name="operate/inv1/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="a" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5,p6,p7" org.eventb.core.prSets="ACCOUNT,CLIENT">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∀ goal (frees a)" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p8">
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⇒ goal" org.eventb.core.prGoal="p8" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p10" org.eventb.core.prHyps="p9">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p10" org.eventb.core.prHyps="p7,p1,p5,p3,p4,p6,p2,p9">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="K" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="balance" org.eventb.core.type="ℙ(ACCOUNT×ℤ)"/>
<org.eventb.core.prIdent name="balance'" org.eventb.core.type="ℙ(ACCOUNT×ℤ)"/>
<org.eventb.core.prIdent name="owner" org.eventb.core.type="ℙ(ACCOUNT×CLIENT)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="finite(CLIENT)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="balance'∈ACCOUNT ⇸ ℕ"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="balance∈ACCOUNT ⇸ ℕ"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="owner∈ACCOUNT ⇸ CLIENT"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="balance'(a)≥0">
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="a∈dom(balance')">
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="a∈dom(balance')⇒balance'(a)≥0">
<org.eventb.core.prIdent name="a" org.eventb.core.type="ACCOUNT"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="K∈ℕ"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀a⦂ACCOUNT·a∈dom(balance)⇒balance(a)≥0"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="finite(ACCOUNT)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀a⦂ACCOUNT·a∈dom(balance')⇒balance'(a)≥0"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<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="com.clearsy.atelierb.provers.core.externalML:1"/>
</org.eventb.core.prProof>
</org.eventb.core.prFile>