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c2_modules.bpr
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c2_modules.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="axm23/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2" org.eventb.core.prSets="MODULE">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p3">
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with credits={15,30,45,60}" org.eventb.core.prHyps="p1">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p2" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p2"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p3" org.eventb.core.prHyps="p1,p2,p4">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p5">
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p5" org.eventb.core.prHyps="p2"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="credits" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="sum" org.eventb.core.type="ℙ(ℙ(MODULE×ℤ)×ℤ)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="sum∈(MODULE ↔ {15,30,45,60}) → ℕ"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="(∅ ⦂ ℙ(MODULE×ℤ))∈dom(sum)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="sum∈ℙ(MODULE × ℤ) ⇸ ℤ"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="credits={15,30,45,60}"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(MODULE×ℤ))∈dom(sum)∧sum∈ℙ(MODULE × ℤ) ⇸ ℤ"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="sum∈(MODULE ↔ credits) → ℕ"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="sum24/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="f,m" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4,p5" org.eventb.core.prSets="MODULE">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="generalized MP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p2">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p6" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p7">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∀ goal (frees f,m)" org.eventb.core.prGoal="p7" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p8">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MODULE"/>
<org.eventb.core.prRule name="r3" 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="p11" org.eventb.core.prHyps="p9,p10">
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p11" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p12">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with credits={15,30,45,60}" org.eventb.core.prHyps="p3">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p5" org.eventb.core.prInfHyps="p13"/>
<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p9" org.eventb.core.prInfHyps="p14"/>
<org.eventb.core.prHypAction name="DESELECT2" org.eventb.core.prHyps="p5,p9"/>
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p12" org.eventb.core.prHyps="p3,p5,p4,p1,p2,p9,p10,p13,p14">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p15">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="eh with credits={15,30,45,60}" org.eventb.core.prHyps="p3">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p5" org.eventb.core.prInfHyps="p13"/>
<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p9" org.eventb.core.prInfHyps="p14"/>
<org.eventb.core.prHypAction name="DESELECT2" org.eventb.core.prHyps="p5,p9"/>
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p15" org.eventb.core.prHyps="p3,p5,p4,p1,p2,p9,p10,p13,p14">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name=")" org.eventb.core.prGoal="p16">
<org.eventb.core.prRule name="r7" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p16" org.eventb.core.prHyps="p9"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="credits" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="sum" org.eventb.core.type="ℙ(ℙ(MODULE×ℤ)×ℤ)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="f∈MODULE ⇸ credits">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="(∅ ⦂ ℙ(MODULE×ℤ))∈dom(sum)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="f∈MODULE ⇸ credits∧m∈dom(f)⇒f∈dom(sum)∧{m} ⩤ f∈dom(sum)∧f∈MODULE ⇸ ℤ">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MODULE"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="sum∈ℙ(MODULE × ℤ) ⇸ ℤ"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="f∈dom(sum)∧{m} ⩤ f∈dom(sum)∧f∈MODULE ⇸ ℤ">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MODULE"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="{m} ⩤ f∈dom(sum)">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MODULE"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀f⦂ℙ(MODULE×ℤ),m⦂MODULE·f∈MODULE ⇸ credits∧m∈dom(f)⇒f∈dom(sum)∧⊤∧{m} ⩤ f∈dom(sum)∧f∈MODULE ⇸ ℤ"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="sum∈(MODULE ↔ {15,30,45,60}) → ℕ"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="m∈dom(f)">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MODULE"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀f⦂ℙ(MODULE×ℤ),m⦂MODULE·f∈MODULE ⇸ credits∧m∈dom(f)⇒f∈dom(sum)∧sum∈ℙ(MODULE × ℤ) ⇸ ℤ∧{m} ⩤ f∈dom(sum)∧f∈MODULE ⇸ ℤ"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="credits={15,30,45,60}"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="f∈MODULE ⇸ ℤ">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="f∈MODULE ⇸ {15,30,45,60}">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="sum(∅ ⦂ ℙ(MODULE×ℤ))=0"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀f⦂ℙ(MODULE×ℤ),m⦂MODULE·f∈MODULE ⇸ credits∧m∈dom(f)⇒f∈dom(sum)∧{m} ⩤ f∈dom(sum)∧f∈MODULE ⇸ ℤ"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="f∈dom(sum)">
<org.eventb.core.prIdent name="f" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="sum∈(MODULE ↔ credits) → ℕ"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.eq:1"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<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="com.clearsy.atelierb.provers.core.externalML:1"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
</org.eventb.core.prProof>
</org.eventb.core.prFile>