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m1_shafts.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/inv2/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" org.eventb.core.prSets="CABINS,SHAFTS">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Partition rewrites in hyp (partition(SHAFTS,{UP},{DOWN}))" 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="p12,p13"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p12,p13"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p14"/>
<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="p11,p8,p6,p1,p7,p5,p4,p2,p9,p12,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.prString name=".pos" org.eventb.core.prSValue=""/>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="FLOORS" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="TOP_FLOOR" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="finite(CABINS)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="CABINS × {UP}∈CABINS → SHAFTS"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="card(CABINS)<card(FLOORS)∗2"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(FLOORS)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="FLOORS=0 ‥ TOP_FLOOR"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="¬UP=DOWN"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="SHAFTS={UP,DOWN}"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="card(FLOORS)=TOP_FLOOR+1"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="TOP_FLOOR=7"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="finite(SHAFTS)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="TOP_FLOOR∈ℕ1"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="CABIN_FLOOR∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.partitionRewrites"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinMovesDown/lower_floor_free/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="c" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3" org.eventb.core.prSets="CABINS,SHAFTS">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Partition rewrites in hyp (partition(SHAFTS,{UP},{DOWN}))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p5,p6"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p5,p6"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="generalized MP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2">
<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="simplification rewrites" org.eventb.core.prGoal="p7" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p10">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p8" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p9"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∀ goal (frees c)" org.eventb.core.prGoal="p10" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p11">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
<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="p13" org.eventb.core.prHyps="p12">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p13" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p14">
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="total function dom substitution in goal" org.eventb.core.prGoal="p14" org.eventb.core.prHyps="p3">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p15">
<org.eventb.core.prRule name="r7" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prGoal="p15" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p16">
<org.eventb.core.prRule name="r8" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p16" org.eventb.core.prHyps=""/>
</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.prExprRef name=".subst" org.eventb.core.prRef="e0"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p17">
<org.eventb.core.prRule name="r9" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p17" org.eventb.core.prHyps="p3"/>
</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=""/>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="shaft" org.eventb.core.type="ℙ(CABINS×SHAFTS)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="∀c⦂CABINS·(c∈dom(floor)⇒c∈dom(shaft)∧shaft∈CABINS ⇸ SHAFTS)∧(c∈dom(floor)∧shaft(c)=DOWN⇒⊤∧⊤)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="¬UP=DOWN">
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="SHAFTS={UP,DOWN}">
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="c∈dom(floor)⇒c∈dom(shaft)∧shaft∈CABINS ⇸ SHAFTS">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c∈dom(floor)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c∈dom(shaft)∧shaft∈CABINS ⇸ SHAFTS">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="c∈dom(shaft)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(floor)⇒c∈dom(shaft)∧shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="c∈CABINS">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂CABINS·(c∈dom(floor)⇒c∈dom(shaft)∧shaft∈CABINS ⇸ SHAFTS)∧(c∈dom(floor)∧shaft(c)=DOWN⇒cabin∈dom(floor)∧floor∈CABINS ⇸ ℤ)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="shaft∈CABINS → SHAFTS"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})">
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="CABINS"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
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<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="cabin∈dom(shaft)"/>
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<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="floor(cabin) − 1∉ran(floor)">
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="shaft∈CABINS → SHAFTS"/>
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<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="SHAFTS={UP,DOWN}">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
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<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c∈dom(floor)">
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<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
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<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="shaft∈CABINS → SHAFTS"/>
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<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
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<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="cabin∈CABINS"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="cabin∈dom(shaft)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="¬floor(cabin)+1∈ran(floor)">
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="shaft∈CABINS → SHAFTS"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="CABINS"/>
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<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.partitionRewrites"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
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<org.eventb.core.lang name="L"/>
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<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p3,p4"/>
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</org.eventb.core.prAnte>
<org.eventb.core.prAnte name="(" org.eventb.core.prGoal="p10">
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="FLOORS" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
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<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
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<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="SHAFTS" org.eventb.core.type="ℙ(SHAFTS)"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="SHAFTS={UP,DOWN}">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="SHAFTS" org.eventb.core.type="ℙ(SHAFTS)"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="cabin∈CABINS"/>
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<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="cabin∈dom(floor)∧floor∈CABINS ⇸ ℤ"/>
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<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="SHAFTS" org.eventb.core.type="ℙ(SHAFTS)"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="shaft" org.eventb.core.type="ℙ(CABINS×SHAFTS)"/>
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<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬UP=DOWN">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="cabin∈dom(shaft)∧shaft∈CABINS ⇸ SHAFTS"/>
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<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
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</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="shaft∈CABINS → SHAFTS"/>
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<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="cabin∈dom(shaft)"/>
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</org.eventb.core.prProof>
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</org.eventb.core.prAnte>
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
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</org.eventb.core.prRule>
</org.eventb.core.prAnte>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
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<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
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<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="shaft" org.eventb.core.type="ℙ(CABINS×SHAFTS)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="SHAFTS={shaft(cabin),shaft(c)}">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="¬shaft(cabin)=shaft(c)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="floor∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="shaft(c)=DOWN">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(shaft)∧shaft(c)=DOWN⇒c∈dom(floor)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬UP=DOWN"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="SHAFTS={UP,DOWN}"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂CABINS·(c∈dom(shaft)⇒⊤)∧(c∈dom(shaft)∧shaft(c)=DOWN⇒c∈dom(floor)∧⊤)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c∈dom(shaft)∧shaft(c)=DOWN⇒c∈dom(floor)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="c∈dom(floor)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c∈dom(shaft)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c∈CABINS">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="shaft(cabin)=UP"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="SHAFTS={shaft(cabin),DOWN}"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂CABINS·(c∈dom(shaft)⇒shaft∈CABINS ⇸ SHAFTS)∧(c∈dom(shaft)∧shaft(c)=DOWN⇒c∈dom(floor)∧floor∈CABINS ⇸ ℤ)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="¬shaft(cabin)=DOWN"/>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="CABINS"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.he:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.partitionRewrites"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinUpToDown/inv2/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" org.eventb.core.prSets="CABINS,SHAFTS">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Partition rewrites in hyp (partition(SHAFTS,{UP},{DOWN}))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p20" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p21,p22"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p21,p22"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p17" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p23"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p10" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p24"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="he with floor(cabin)=TOP_FLOOR" org.eventb.core.prHyps="p1">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p24" org.eventb.core.prInfHyps="p25"/>
<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p24"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="he with shaft(cabin)=UP" org.eventb.core.prHyps="p18">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p21" org.eventb.core.prInfHyps="p26"/>
<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p22" org.eventb.core.prInfHyps="p27"/>
<org.eventb.core.prHypAction name="DESELECT2" org.eventb.core.prHyps="p21,p22"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p15,p11,p8,p2,p9,p6,p5,p16,p12,p4,p19,p1,p3,p7,p18,p13,p14,p21,p22,p23,p24,p25,p26,p27">
<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.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="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="FLOORS" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="TOP_FLOOR" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="shaft" org.eventb.core.type="ℙ(CABINS×SHAFTS)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="floor(cabin)=TOP_FLOOR"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="finite(FLOORS)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="TOP_FLOOR=7"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="finite(SHAFTS)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="cabin∈dom(shaft)"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="CABIN_FLOOR∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="shaft{cabin ↦ DOWN}∈CABINS → SHAFTS"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="shaft(cabin)=UP"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="SHAFTS={shaft(cabin),DOWN}"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(shaft)∧shaft(c)=DOWN⇒¬floor(c)=floor(cabin)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="shaft∈CABINS → SHAFTS"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="finite(CABINS)"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(shaft)∧shaft(c)=DOWN⇒¬floor(c)=TOP_FLOOR"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="floor∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="card(CABINS)<card(FLOORS)∗2"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="FLOORS=0 ‥ TOP_FLOOR"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="¬UP=DOWN"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="SHAFTS={UP,DOWN}"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="card(FLOORS)=TOP_FLOOR+1"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(shaft)∧shaft(c)=DOWN⇒floor(c)≠TOP_FLOOR"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="TOP_FLOOR∈ℕ1"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="¬shaft(cabin)=DOWN"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.he:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.partitionRewrites"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinDownToUp/grd1/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1" org.eventb.core.prSets="CABINS">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Partition rewrites in hyp (partition(SHAFTS,{UP},{DOWN}))" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3,p4"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p3,p4"/>
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<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p9">
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
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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.prRule>
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</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue=""/>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="FLOORS" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
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<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬UP=DOWN">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="SHAFTS" org.eventb.core.type="ℙ(SHAFTS)"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="SHAFTS={UP,DOWN}">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="SHAFTS" org.eventb.core.type="ℙ(SHAFTS)"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="cabin∈CABINS"/>
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<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="cabin∈dom(floor)∧floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="SHAFTS" org.eventb.core.type="ℙ(SHAFTS)"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="CABINS"/>
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<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
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<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinDownToUp/grd2/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1" org.eventb.core.prSets="CABINS,SHAFTS">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Partition rewrites in hyp (partition(SHAFTS,{UP},{DOWN}))" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3,p4"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
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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.prString name=".pos" org.eventb.core.prSValue=""/>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="shaft" org.eventb.core.type="ℙ(CABINS×SHAFTS)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬UP=DOWN">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="cabin∈dom(shaft)∧shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="SHAFTS={UP,DOWN}">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="cabin∈CABINS"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="shaft∈CABINS → SHAFTS"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})">
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="cabin∈dom(shaft)"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="CABINS"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.conj:0"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.partitionRewrites"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinDownToUp/grd3/WD" org.eventb.core.confidence="1000" org.eventb.core.prFresh="c" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3,p4" org.eventb.core.prSets="CABINS,SHAFTS">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Partition rewrites in hyp (partition(SHAFTS,{UP},{DOWN}))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p6,p7"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p6,p7"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="generalized MP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p2,p4">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p8">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p8" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p11">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p9" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p10"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∀ goal (frees c)" org.eventb.core.prGoal="p11" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p12">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⇒ goal" org.eventb.core.prGoal="p12" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p15" org.eventb.core.prHyps="p13,p14">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="he with shaft(cabin)=DOWN" org.eventb.core.prHyps="p3">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p6" org.eventb.core.prInfHyps="p16"/>
<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p7" org.eventb.core.prInfHyps="p17"/>
<org.eventb.core.prHypAction name="DESELECT2" org.eventb.core.prHyps="p6,p7"/>
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<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p16" org.eventb.core.prInfHyps="p18"/>
<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p17" org.eventb.core.prInfHyps="p19"/>
<org.eventb.core.prHypAction name="DESELECT2" org.eventb.core.prHyps="p16,p17"/>
<org.eventb.core.prRule name="r6" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="total function dom substitution in goal" org.eventb.core.prGoal="p15" org.eventb.core.prHyps="p1">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p20">
<org.eventb.core.prRule name="r7" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prGoal="p20" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p21">
<org.eventb.core.prRule name="r8" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p21" org.eventb.core.prHyps=""/>
</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.prExprRef name=".subst" org.eventb.core.prRef="e0"/>
</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.prRule>
</org.eventb.core.prAnte>
<org.eventb.core.prString name=".pos" org.eventb.core.prSValue=""/>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="FLOORS" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="shaft" org.eventb.core.type="ℙ(CABINS×SHAFTS)"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="¬shaft(c)=shaft(cabin)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="floor∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="SHAFTS={shaft(c),shaft(cabin)}">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(shaft)∧shaft(c)=UP⇒c∈dom(floor)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬UP=DOWN"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="SHAFTS={UP,DOWN}"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀c⦂CABINS·(c∈dom(shaft)⇒shaft∈CABINS ⇸ SHAFTS)∧(c∈dom(shaft)∧shaft(c)=UP⇒c∈dom(floor)∧floor∈CABINS ⇸ ℤ)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="shaft(cabin)=DOWN"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="c∈dom(floor)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="shaft∈CABINS ⇸ SHAFTS"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="c∈dom(shaft)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="c∈dom(shaft)∧shaft(c)=UP⇒c∈dom(floor)">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)">
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="c∈CABINS">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="∀c⦂CABINS·(c∈dom(shaft)⇒⊤)∧(c∈dom(shaft)∧shaft(c)=UP⇒c∈dom(floor)∧⊤)"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="shaft(c)=UP">
<org.eventb.core.prIdent name="c" org.eventb.core.type="CABINS"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="¬UP=shaft(cabin)"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="partition(SHAFTS,{UP},{DOWN})"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="SHAFTS={UP,shaft(cabin)}"/>
<org.eventb.core.prExpr name="e0" org.eventb.core.expression="CABINS"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.impI"/>
<org.eventb.core.prReas name="r8" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.allI"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.he:1"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.partitionRewrites"/>
<org.eventb.core.prReas name="r6" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
<org.eventb.core.prReas name="r7" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinDownToUp/inv2/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" org.eventb.core.prSets="CABINS,SHAFTS">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="Partition rewrites in hyp (partition(SHAFTS,{UP},{DOWN}))" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p20" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p21,p22"/>
<org.eventb.core.prHypAction name="SELECT1" org.eventb.core.prHyps="p21,p22"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p18" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p23"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p5" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p24"/>
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<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p21" org.eventb.core.prInfHyps="p25"/>
<org.eventb.core.prHypAction name="FORWARD_INF1" org.eventb.core.prHyps="p22" org.eventb.core.prInfHyps="p26"/>
<org.eventb.core.prHypAction name="DESELECT2" org.eventb.core.prHyps="p21,p22"/>
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</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="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="DOWN" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="FLOORS" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="TOP_FLOOR" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="UP" org.eventb.core.type="SHAFTS"/>
<org.eventb.core.prIdent name="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="shaft" org.eventb.core.type="ℙ(CABINS×SHAFTS)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="finite(FLOORS)"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒¬CABIN_FLOOR(c)∈ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="TOP_FLOOR=7"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="finite(SHAFTS)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="cabin∈dom(shaft)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="shaft{cabin ↦ UP}∈CABINS → SHAFTS"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="CABIN_FLOOR∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="¬UP=shaft(cabin)"/>
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<org.eventb.core.prPred name="p1" org.eventb.core.predicate="finite(CABINS)"/>