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m0_cabins.bpr
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m0_cabins.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/up_type/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p0" org.eventb.core.prSets="CABINS">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="hyp" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p0"/>
<org.eventb.core.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prIdent name="FLOORS" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="CABIN_FLOOR∈CABINS → FLOORS"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.hyp"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinMovesUp/not_at_top_floor/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">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p4">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="total function dom substitution in goal" org.eventb.core.prGoal="p4" org.eventb.core.prHyps="p1">
<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="type rewrites" org.eventb.core.prGoal="p5" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p6" 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="p7">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p7" org.eventb.core.prHyps="p1"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</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)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="floor∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p2" 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="p7" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="cabin∈CABINS"/>
<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.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.prExpr name="e0" org.eventb.core.expression="CABINS"/>
<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.conj:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinMovesUp/up_type/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" org.eventb.core.prSets="CABINS">
<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="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="ML" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p10,p9,p7,p1,p8,p5,p4,p11,p3,p12,p2,p6,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.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<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="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="finite(CABINS)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="floor∈CABINS → FLOORS"/>
<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="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="FLOORS=0 ‥ TOP_FLOOR"/>
<org.eventb.core.prPred name="p8" 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="p9" org.eventb.core.predicate="TOP_FLOOR=7"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="TOP_FLOOR∈ℕ1"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="CABIN_FLOOR∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="TOP_FLOOR≥floor(cabin)+1"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="floor{cabin ↦ floor(cabin)+1}∈CABINS → FLOORS"/>
<org.eventb.core.prReas name="r1" 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="CabinMovesUp/move_up/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="CABINS">
<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="p1,p2">
<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="simplification rewrites" org.eventb.core.prGoal="p3" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p5"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p6" org.eventb.core.prHyps=""/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<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.prPred name="p1" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="⊤∧⊤"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p4" 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="p2" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<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="p0" org.eventb.core.predicate="cabin∈dom(floor)∧floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<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.trueGoal"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinMovesDown/not_at_ground_floor/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">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p3"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="∧ goal" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p4">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="total function dom substitution in goal" org.eventb.core.prGoal="p4" org.eventb.core.prHyps="p1">
<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="type rewrites" org.eventb.core.prGoal="p5" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prRule name="r4" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p6" 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="p7">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p7" org.eventb.core.prHyps="p1"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</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)"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="floor∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p2" 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="p7" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="cabin∈CABINS"/>
<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.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.prExpr name="e0" org.eventb.core.expression="CABINS"/>
<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.conj:0"/>
<org.eventb.core.prReas name="r5" org.eventb.core.prRID="org.eventb.core.seqprover.isFunGoal"/>
<org.eventb.core.prReas name="r4" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.totalDom:2"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="CabinMovesDown/up_type/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" org.eventb.core.prSets="CABINS">
<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="p12" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p14"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="ML" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p10,p9,p7,p1,p8,p5,p4,p11,p3,p13,p2,p6,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.prIdent name="CABIN_FLOOR" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<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="cabin" org.eventb.core.type="CABINS"/>
<org.eventb.core.prIdent name="floor" org.eventb.core.type="ℙ(CABINS×ℤ)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="finite(CABINS)"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="floor∈CABINS → FLOORS"/>
<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="floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="FLOORS=0 ‥ TOP_FLOOR"/>
<org.eventb.core.prPred name="p8" 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="p9" org.eventb.core.predicate="TOP_FLOOR=7"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="TOP_FLOOR∈ℕ1"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="CABIN_FLOOR∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="∀c⦂CABINS·c∈dom(CABIN_FLOOR)⇒CABIN_FLOOR(c)∉ran({c} ⩤ CABIN_FLOOR)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="floor{cabin ↦ floor(cabin) − 1}∈CABINS → FLOORS"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="0≤floor(cabin) − 1"/>
<org.eventb.core.prReas name="r1" 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="CabinMovesDown/move_down/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="CABINS">
<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="p1,p2">
<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="simplification rewrites" org.eventb.core.prGoal="p3" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p5"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p6" org.eventb.core.prHyps=""/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<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.prPred name="p1" org.eventb.core.predicate="cabin∈dom(floor)"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="⊤∧⊤"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p4" 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="p2" org.eventb.core.predicate="floor∈CABINS ⇸ ℤ"/>
<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="p0" org.eventb.core.predicate="cabin∈dom(floor)∧floor∈CABINS ⇸ ℤ"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<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.trueGoal"/>
</org.eventb.core.prProof>
</org.eventb.core.prFile>