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<org.eventb.core.prFile version="1">
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<org.eventb.core.prIdent name="MEDIUM" org.eventb.core.type="LEVEL"/>
<org.eventb.core.prIdent name="MINE" org.eventb.core.type="ℙ(MINE_SET)"/>
<org.eventb.core.prIdent name="OFF" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="ON" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MINE_SET"/>
<org.eventb.core.prIdent name="methane" org.eventb.core.type="ℙ(MINE_SET×BOOL)"/>
<org.eventb.core.prIdent name="pump" org.eventb.core.type="ℙ(MINE_SET×ONOFF)"/>
<org.eventb.core.prIdent name="waterLevel" org.eventb.core.type="ℙ(MINE_SET×LEVEL)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="m∈dom(pump)∧pump∈MINE_SET ⇸ ONOFF"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="methane∈MINE → BOOL"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="dom(waterLevel)=MINE"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="m∈MINE"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="waterLevel∈MINE_SET ⇸ LEVEL"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="waterLevel(m)=LOW"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="partition(MINE_SET,{M})"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="m∈dom(waterLevel)"/>
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<org.eventb.core.prPred name="p9" org.eventb.core.predicate="dom(methane)=MINE"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="MINE∈ℙ(MINE_SET)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="waterLevel∈MINE → LEVEL"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="dom(pump)=MINE"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p0"/>
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
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<org.eventb.core.prIdent name="MEDIUM" org.eventb.core.type="LEVEL"/>
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<org.eventb.core.prIdent name="ON" org.eventb.core.type="ONOFF"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="partition(MINE_SET,{M})">
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<org.eventb.core.prIdent name="MINE_SET" org.eventb.core.type="ℙ(MINE_SET)"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="LEVEL" org.eventb.core.type="ℙ(LEVEL)"/>
<org.eventb.core.prIdent name="LOW" org.eventb.core.type="LEVEL"/>
<org.eventb.core.prIdent name="MEDIUM" org.eventb.core.type="LEVEL"/>
</org.eventb.core.prPred>
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<org.eventb.core.prIdent name="LOW" org.eventb.core.type="LEVEL"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="ONOFF={ON,OFF}">
<org.eventb.core.prIdent name="OFF" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="ON" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="ONOFF" org.eventb.core.type="ℙ(ONOFF)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬MEDIUM=HIGH">
<org.eventb.core.prIdent name="HIGH" org.eventb.core.type="LEVEL"/>
<org.eventb.core.prIdent name="MEDIUM" org.eventb.core.type="LEVEL"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="LEVEL={LOW,MEDIUM,HIGH}">
<org.eventb.core.prIdent name="HIGH" org.eventb.core.type="LEVEL"/>
<org.eventb.core.prIdent name="LEVEL" org.eventb.core.type="ℙ(LEVEL)"/>
<org.eventb.core.prIdent name="LOW" org.eventb.core.type="LEVEL"/>
<org.eventb.core.prIdent name="MEDIUM" org.eventb.core.type="LEVEL"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="MINE∈ℙ(MINE_SET)">
<org.eventb.core.prIdent name="MINE" org.eventb.core.type="ℙ(MINE_SET)"/>
<org.eventb.core.prIdent name="MINE_SET" org.eventb.core.type="ℙ(MINE_SET)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="MINE_SET={M}">
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<org.eventb.core.prIdent name="MINE_SET" org.eventb.core.type="ℙ(MINE_SET)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="partition(ONOFF,{ON},{OFF})">
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<org.eventb.core.prIdent name="ON" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="ONOFF" org.eventb.core.type="ℙ(ONOFF)"/>
</org.eventb.core.prPred>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="methane_detected/act1/SIM" 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" org.eventb.core.prSets="LEVEL,MINE_SET,ONOFF">
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<org.eventb.core.prIdent name="MINE" org.eventb.core.type="ℙ(MINE_SET)"/>
<org.eventb.core.prIdent name="OFF" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="ON" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MINE_SET"/>
<org.eventb.core.prIdent name="methane" org.eventb.core.type="ℙ(MINE_SET×BOOL)"/>
<org.eventb.core.prIdent name="pump" org.eventb.core.type="ℙ(MINE_SET×ONOFF)"/>
<org.eventb.core.prIdent name="waterLevel" org.eventb.core.type="ℙ(MINE_SET×LEVEL)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="methane(m)=TRUE"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="methane∈MINE → BOOL"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="dom(waterLevel)=MINE"/>
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<org.eventb.core.prPred name="p5" org.eventb.core.predicate="(pump(m)=OFF∧pump{m ↦ OFF}=pump{m ↦ ON})∨(m∈dom(pump)∧pump∈MINE_SET ⇸ ONOFF)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="pump∈MINE_SET ⇸ ONOFF"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="methane∈MINE_SET ⇸ BOOL"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="m∈dom(methane)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="partition(MINE_SET,{M})"/>
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<org.eventb.core.prPred name="p15" org.eventb.core.predicate="pump(m)=ON"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="dom(pump)=MINE"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="waterLevel∈MINE → LEVEL"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(pump(m)=OFF∧pump{m ↦ OFF}=pump{m ↦ ON})∨(pump(m)=ON∧pump{m ↦ OFF}=pump{m ↦ OFF})"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="m∈dom(pump)"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="pump∈MINE → ONOFF"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="partition(ONOFF,{ON},{OFF})"/>
</org.eventb.core.prProof>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="M" org.eventb.core.type="MINE_SET"/>
<org.eventb.core.prIdent name="MEDIUM" org.eventb.core.type="LEVEL"/>
<org.eventb.core.prIdent name="MINE" org.eventb.core.type="ℙ(MINE_SET)"/>
<org.eventb.core.prIdent name="OFF" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="ON" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MINE_SET"/>
<org.eventb.core.prIdent name="methane" org.eventb.core.type="ℙ(MINE_SET×BOOL)"/>
<org.eventb.core.prIdent name="pump" org.eventb.core.type="ℙ(MINE_SET×ONOFF)"/>
<org.eventb.core.prIdent name="waterLevel" org.eventb.core.type="ℙ(MINE_SET×LEVEL)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="partition(MINE_SET,{M})"/>
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</org.eventb.core.prProof>
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</org.eventb.core.prRule>
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<org.eventb.core.prIdent name="MINE" org.eventb.core.type="ℙ(MINE_SET)"/>
<org.eventb.core.prIdent name="OFF" org.eventb.core.type="ONOFF"/>
<org.eventb.core.prIdent name="ON" org.eventb.core.type="ONOFF"/>
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<org.eventb.core.prIdent name="methane" org.eventb.core.type="ℙ(MINE_SET×BOOL)"/>
<org.eventb.core.prIdent name="pump" org.eventb.core.type="ℙ(MINE_SET×ONOFF)"/>
<org.eventb.core.prIdent name="waterLevel" org.eventb.core.type="ℙ(MINE_SET×LEVEL)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="methane∈MINE → BOOL"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="dom(methane)=MINE"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="dom(waterLevel)=MINE"/>
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</org.eventb.core.prProof>
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<org.eventb.core.prIdent name="methane" org.eventb.core.type="ℙ(MINE_SET×BOOL)"/>
<org.eventb.core.prIdent name="pump" org.eventb.core.type="ℙ(MINE_SET×ONOFF)"/>
<org.eventb.core.prIdent name="waterLevel" org.eventb.core.type="ℙ(MINE_SET×LEVEL)"/>
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<org.eventb.core.prPred name="p3" org.eventb.core.predicate="m∈MINE"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="pump∈MINE_SET ⇸ ONOFF"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="partition(MINE_SET,{M})"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="partition(LEVEL,{LOW},{MEDIUM},{HIGH})"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="dom(methane)=MINE"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="MINE∈ℙ(MINE_SET)"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="waterLevel∈MINE → LEVEL"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="dom(pump)=MINE"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="pump(m)=ON"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="m∈dom(pump)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="pump∈MINE → ONOFF"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="partition(ONOFF,{ON},{OFF})"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="m∈dom(methane)∧methane∈MINE_SET ⇸ BOOL"/>
</org.eventb.core.prProof>
</org.eventb.core.prFile>
