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m4.bpr
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m4.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/inv1/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="COR,UNIT">
<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.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p1" org.eventb.core.prHyps="p3" org.eventb.core.prInfHyps="p2"/>
<org.eventb.core.prRule name="r1" 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="p13">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p5,p6,p7,p8"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p9,p10,p11,p12"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p13" 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="DEADLINE" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="POSITION" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="finite(VIEW)">
<org.eventb.core.prIdent name="VIEW" org.eventb.core.type="ℙ(VIEW)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="finite(UNIT)∧finite(ORG)∧finite(ROLE)∧finite(EMPLOYEE)∧finite(CONTEXT)">
<org.eventb.core.prIdent name="CONTEXT" org.eventb.core.type="ℙ(CONTEXT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="ORG" org.eventb.core.type="ℙ(ORG)"/>
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="finite(ACTIVITY)∧finite(ACTION)∧finite(VIEW)∧finite(RESOURCE)">
<org.eventb.core.prIdent name="ACTION" org.eventb.core.type="ℙ(ACTION)"/>
<org.eventb.core.prIdent name="ACTIVITY" org.eventb.core.type="ℙ(ACTIVITY)"/>
<org.eventb.core.prIdent name="RESOURCE" org.eventb.core.type="ℙ(RESOURCE)"/>
<org.eventb.core.prIdent name="VIEW" org.eventb.core.type="ℙ(VIEW)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="finite(CONTEXT)">
<org.eventb.core.prIdent name="CONTEXT" org.eventb.core.type="ℙ(CONTEXT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="finite(ACTION)">
<org.eventb.core.prIdent name="ACTION" org.eventb.core.type="ℙ(ACTION)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="finite(EMPLOYEE)">
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="finite(UNIT)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(COR×UNIT×ℤ×ℤ))⊆COR × UNIT × POSITION × DEADLINE"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="finite(RESOURCE)">
<org.eventb.core.prIdent name="RESOURCE" org.eventb.core.type="ℙ(RESOURCE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="finite(ORG)">
<org.eventb.core.prIdent name="ORG" org.eventb.core.type="ℙ(ORG)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(ACTIVITY)">
<org.eventb.core.prIdent name="ACTIVITY" org.eventb.core.type="ℙ(ACTIVITY)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="finite(ROLE)">
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="finite(UNIT)∧finite(ORG)∧finite(ROLE)∧finite(EMPLOYEE)∧⊤">
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="ORG" org.eventb.core.type="ℙ(ORG)"/>
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL4"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="Assign_CoR_to_Organization/inv1/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2" org.eventb.core.prSets="COR,ORG,UNIT">
<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="p24">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4,p5,p6,p7,p8"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p9" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p10,p11,p12,p13"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p14" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p15"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p16" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p17"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p18" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p19"/>
<org.eventb.core.prHypAction name="REWRITE5" org.eventb.core.prHidden="p2" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p20,p21"/>
<org.eventb.core.prHypAction name="REWRITE6" org.eventb.core.prHidden="p22" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p23"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="generalized MP" org.eventb.core.prGoal="p24" org.eventb.core.prHyps="p21,p1,p20">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p25">
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p25" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p26">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p26" org.eventb.core.prHyps=""/>
</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="Approver1" org.eventb.core.type="ℙ(COR×(UNIT×ORG))"/>
<org.eventb.core.prIdent name="OU1" org.eventb.core.type="ℙ(UNIT×ORG)"/>
<org.eventb.core.prIdent name="cor" org.eventb.core.type="COR"/>
<org.eventb.core.prIdent name="ou" org.eventb.core.type="UNIT×ORG"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="Approver1∪{cor ↦ ou}⊆COR × OU1"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="Approver1⊆COR × OU1"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="finite(UNIT)∧finite(ORG)∧finite(ROLE)∧finite(EMPLOYEE)∧finite(CONTEXT)">
<org.eventb.core.prIdent name="CONTEXT" org.eventb.core.type="ℙ(CONTEXT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="∀u1⦂UNIT,u2⦂UNIT,e⦂EMPLOYEE·u1 ↦ u2∈UH1∧e ↦ u1∈EA1⇒e ↦ u2∉EA1">
<org.eventb.core.prIdent name="EA1" org.eventb.core.type="ℙ(EMPLOYEE×UNIT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀us⦂UNIT,um⦂UNIT·us ↦ um∈UH1⇒(us∈dom(OU1)∧um∈dom(OU1)⇒OU1(us)=OU1(um))">
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="∀u1⦂UNIT,u2⦂UNIT,e⦂EMPLOYEE·u1 ↦ u2∈UH1∧e ↦ u1∈EA1⇒¬e ↦ u2∈EA1">
<org.eventb.core.prIdent name="EA1" org.eventb.core.type="ℙ(EMPLOYEE×UNIT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="finite(EMPLOYEE)">
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(ORG)"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="finite(ROLE)">
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="∀u⦂UNIT,org⦂ORG,role⦂ROLE·u ↦ (role ↦ org)∈UR1⇒(u∈dom(OU1)⇒OU1(u)=org)">
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
<org.eventb.core.prIdent name="UR1" org.eventb.core.type="ℙ(UNIT×(ROLE×ORG))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="cor ↦ ou∉Approver1"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="finite(VIEW)">
<org.eventb.core.prIdent name="VIEW" org.eventb.core.type="ℙ(VIEW)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="cor∈COR"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀u⦂UNIT,org⦂ORG,role⦂ROLE·u ↦ (role ↦ org)∈UR1⇒(OU1[{u}]≠(∅ ⦂ ℙ(ORG))⇒OU1(u)=org)">
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
<org.eventb.core.prIdent name="UR1" org.eventb.core.type="ℙ(UNIT×(ROLE×ORG))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="ou∈OU1"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="finite(ACTIVITY)∧finite(ACTION)∧finite(VIEW)∧finite(RESOURCE)">
<org.eventb.core.prIdent name="ACTION" org.eventb.core.type="ℙ(ACTION)"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀u1⦂UNIT,u2⦂UNIT,e⦂EMPLOYEE·u1 ↦ u2∈UH1∧e ↦ u1∈EA1⇒¬e ↦ u2∈EA1">
<org.eventb.core.prIdent name="EA1" org.eventb.core.type="ℙ(EMPLOYEE×UNIT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
<org.eventb.core.prIdent name="UNIT" org.eventb.core.type="ℙ(UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="finite(CONTEXT)">
<org.eventb.core.prIdent name="CONTEXT" org.eventb.core.type="ℙ(CONTEXT)"/>
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<org.eventb.core.prPred name="p6" org.eventb.core.predicate="finite(ACTION)">
<org.eventb.core.prIdent name="ACTION" org.eventb.core.type="ℙ(ACTION)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="finite(EMPLOYEE)">
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="finite(UNIT)">
<org.eventb.core.prIdent name="UNIT" org.eventb.core.type="ℙ(UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="finite(RESOURCE)">
<org.eventb.core.prIdent name="RESOURCE" org.eventb.core.type="ℙ(RESOURCE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="finite(ORG)">
<org.eventb.core.prIdent name="ORG" org.eventb.core.type="ℙ(ORG)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(ACTIVITY)">
<org.eventb.core.prIdent name="ACTIVITY" org.eventb.core.type="ℙ(ACTIVITY)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="∀us⦂UNIT,um⦂UNIT·us ↦ um∈UH1⇒(OU1[{us}]≠(∅ ⦂ ℙ(ORG))∧OU1[{um}]≠(∅ ⦂ ℙ(ORG))⇒OU1(us)=OU1(um))">
<org.eventb.core.prIdent name="ORG" org.eventb.core.type="ℙ(ORG)"/>
<org.eventb.core.prIdent name="OU1" org.eventb.core.type="ℙ(UNIT×ORG)"/>
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
<org.eventb.core.prIdent name="UNIT" org.eventb.core.type="ℙ(UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="finite(ROLE)">
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="PCA1=PCA1"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="finite(UNIT)∧finite(ORG)∧finite(ROLE)∧finite(EMPLOYEE)∧⊤">
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="ORG" org.eventb.core.type="ℙ(ORG)"/>
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
<org.eventb.core.prIdent name="UNIT" org.eventb.core.type="ℙ(UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀cor⦂COR,u1⦂UNIT,p1⦂ℤ,d1⦂ℤ,u2⦂UNIT,p2⦂ℤ,d2⦂ℤ·cor ↦ u1 ↦ p1 ↦ d1∈CA1∧cor ↦ u2 ↦ p2 ↦ d2∈CA1∧¬u1=u2⇒(u1∈dom(OU1)∧u2∈dom(OU1)⇒OU1(u1)=OU1(u2))">
<org.eventb.core.prIdent name="CA1" org.eventb.core.type="ℙ(COR×UNIT×ℤ×ℤ)"/>
<org.eventb.core.prIdent name="ORG" org.eventb.core.type="ℙ(ORG)"/>
<org.eventb.core.prIdent name="OU1" org.eventb.core.type="ℙ(UNIT×ORG)"/>
<org.eventb.core.prIdent name="UNIT" org.eventb.core.type="ℙ(UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL4"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="Abstract_Model_Generation/act9/FIS" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="ORG,PERMISSION,UNIT">
<org.eventb.core.lang name="L">
<org.eventb.theory.core.scNewOperatorDefinition name="seq" org.eventb.core.label="seq" org.eventb.core.predicate="⊤" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#(" org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.closed" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="ℙ(ℙ(ℤ×A))" org.eventb.theory.core.wd="∀n⦂ℤ,f⦂ℙ(ℤ×A)·(n∈ℕ∧f∈1 ‥ n → a)∨¬n∈ℕ∨¬f∈1 ‥ n → a">
<org.eventb.theory.core.scOperatorArgument name="a" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#(|org.eventb.theory.core.operatorArgument#'" org.eventb.core.type="ℙ(A)"/>
<org.eventb.theory.core.scDirectOperatorDefinition name="(" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#(|org.eventb.theory.core.directOperatorDefinition#(" org.eventb.theory.core.formula="{n⦂ℤ,f⦂ℙ(ℤ×A)·n∈ℕ∧f∈1 ‥ n → a ∣ f}"/>
</org.eventb.theory.core.scNewOperatorDefinition>
<org.eventb.theory.core.scNewOperatorDefinition name="seqSize" org.eventb.core.label="seqSize" org.eventb.core.predicate="s∈seq(A)" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#)" org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.closed" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="ℤ" org.eventb.theory.core.wd="finite(s)">
<org.eventb.theory.core.scOperatorArgument name="s" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#)|org.eventb.theory.core.operatorArgument#'" org.eventb.core.type="ℙ(ℤ×A)"/>
<org.eventb.theory.core.scDirectOperatorDefinition name="(" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#)|org.eventb.theory.core.directOperatorDefinition#(" org.eventb.theory.core.formula="card(s)"/>
</org.eventb.theory.core.scNewOperatorDefinition>
<org.eventb.theory.core.scNewOperatorDefinition name="emptySeq" org.eventb.core.label="emptySeq" org.eventb.core.predicate="⊤" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#5" org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.atomicExpr" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="ℙ(A)" org.eventb.theory.core.wd="⊤">
<org.eventb.theory.core.scDirectOperatorDefinition name="'" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#5|org.eventb.theory.core.directOperatorDefinition#'" org.eventb.theory.core.formula="∅ ⦂ ℙ(A)"/>
</org.eventb.theory.core.scNewOperatorDefinition>
<org.eventb.theory.core.scNewOperatorDefinition name="seqHead" org.eventb.core.label="seqHead" org.eventb.core.predicate="s∈seq(A)∧s≠(emptySeq ⦂ ℙ(ℤ×A))" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#+" org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.closed" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="A" org.eventb.theory.core.wd="1∈dom(s)∧s∈ℤ ⇸ A">
<org.eventb.theory.core.scOperatorArgument name="s" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#+|org.eventb.theory.core.operatorArgument#'" org.eventb.core.type="ℙ(ℤ×A)"/>
<org.eventb.theory.core.scDirectOperatorDefinition name=")" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#+|org.eventb.theory.core.directOperatorDefinition#)" org.eventb.theory.core.formula="s(1)"/>
</org.eventb.theory.core.scNewOperatorDefinition>
<org.eventb.theory.core.scNewOperatorDefinition name="seqTail" org.eventb.core.label="seqTail" org.eventb.core.predicate="s∈seq(A)∧s≠(emptySeq ⦂ ℙ(ℤ×A))" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#," org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.closed" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="ℙ(ℤ×A)" org.eventb.theory.core.wd="∀i⦂ℤ·finite(s)∧(i∈1 ‥ card(s) − 1⇒i+1∈dom(s)∧s∈ℤ ⇸ A)">
<org.eventb.theory.core.scOperatorArgument name="s" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#,|org.eventb.theory.core.operatorArgument#'" org.eventb.core.type="ℙ(ℤ×A)"/>
<org.eventb.theory.core.scDirectOperatorDefinition name=")" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#,|org.eventb.theory.core.directOperatorDefinition#)" org.eventb.theory.core.formula="λi⦂ℤ·i∈1 ‥ card(s) − 1 ∣ s(i+1)"/>
</org.eventb.theory.core.scNewOperatorDefinition>
<org.eventb.theory.core.scNewOperatorDefinition name="seqPrepend" org.eventb.core.label="seqPrepend" org.eventb.core.predicate="s∈seq(A)" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#-" org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.closed" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="ℙ(ℤ×A)" org.eventb.theory.core.wd="∀i⦂ℤ·i∈2 ‥ seqSize(s)+1⇒i − 1∈dom(s)∧s∈ℤ ⇸ A">
<org.eventb.theory.core.scOperatorArgument name="s" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#-|org.eventb.theory.core.operatorArgument#'" org.eventb.core.type="ℙ(ℤ×A)"/>
<org.eventb.theory.core.scOperatorArgument name="e" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#-|org.eventb.theory.core.operatorArgument#(" org.eventb.core.type="A"/>
<org.eventb.theory.core.scDirectOperatorDefinition name=")" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#-|org.eventb.theory.core.directOperatorDefinition#)" org.eventb.theory.core.formula="{1 ↦ e}∪(λi⦂ℤ·i∈2 ‥ seqSize(s)+1 ∣ s(i − 1))"/>
</org.eventb.theory.core.scNewOperatorDefinition>
<org.eventb.theory.core.scNewOperatorDefinition name="seqAppend" org.eventb.core.label="seqAppend" org.eventb.core.predicate="s∈seq(A)" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#." org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.closed" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="ℙ(ℤ×A)" org.eventb.theory.core.wd="finite(s)">
<org.eventb.theory.core.scOperatorArgument name="s" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#.|org.eventb.theory.core.operatorArgument#'" org.eventb.core.type="ℙ(ℤ×A)"/>
<org.eventb.theory.core.scOperatorArgument name="e" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#.|org.eventb.theory.core.operatorArgument#(" org.eventb.core.type="A"/>
<org.eventb.theory.core.scDirectOperatorDefinition name=")" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#.|org.eventb.theory.core.directOperatorDefinition#)" org.eventb.theory.core.formula="s∪{card(s)+1 ↦ e}"/>
</org.eventb.theory.core.scNewOperatorDefinition>
</org.eventb.core.lang>
<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="p18">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p1" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p2,p3,p4,p5,p6"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p7" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8,p9,p10,p11"/>
<org.eventb.core.prHypAction name="REWRITE2" org.eventb.core.prHidden="p12" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p13"/>
<org.eventb.core.prHypAction name="REWRITE3" org.eventb.core.prHidden="p14" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p15"/>
<org.eventb.core.prHypAction name="REWRITE4" org.eventb.core.prHidden="p16" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p17"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p18" org.eventb.core.prHyps=""/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="COR1" org.eventb.core.type="ℙ(ORG×ℙ(ℤ×UNIT))"/>
<org.eventb.core.prIdent name="perms" org.eventb.core.type="ℙ(PERMISSION)"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀u⦂UNIT,org⦂ORG,role⦂ROLE·u ↦ (role ↦ org)∈UR1⇒(u∈dom(OU1)⇒OU1(u)=org)">
<org.eventb.core.prIdent name="OU1" org.eventb.core.type="ℙ(UNIT×ORG)"/>
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
<org.eventb.core.prIdent name="UR1" org.eventb.core.type="ℙ(UNIT×(ROLE×ORG))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="finite(VIEW)">
<org.eventb.core.prIdent name="VIEW" org.eventb.core.type="ℙ(VIEW)"/>
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<org.eventb.core.prPred name="p14" org.eventb.core.predicate="∀u⦂UNIT,org⦂ORG,role⦂ROLE·u ↦ (role ↦ org)∈UR1⇒(OU1[{u}]≠(∅ ⦂ ℙ(ORG))⇒OU1(u)=org)">
<org.eventb.core.prIdent name="OU1" org.eventb.core.type="ℙ(UNIT×ORG)"/>
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
<org.eventb.core.prIdent name="UR1" org.eventb.core.type="ℙ(UNIT×(ROLE×ORG))"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="finite(UNIT)∧finite(ORG)∧finite(ROLE)∧finite(EMPLOYEE)∧finite(CONTEXT)">
<org.eventb.core.prIdent name="CONTEXT" org.eventb.core.type="ℙ(CONTEXT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="ROLE" org.eventb.core.type="ℙ(ROLE)"/>
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<org.eventb.core.prPred name="p16" org.eventb.core.predicate="∀u1⦂UNIT,u2⦂UNIT,e⦂EMPLOYEE·u1 ↦ u2∈UH1∧e ↦ u1∈EA1⇒e ↦ u2∉EA1">
<org.eventb.core.prIdent name="EA1" org.eventb.core.type="ℙ(EMPLOYEE×UNIT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
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<org.eventb.core.prPred name="p13" org.eventb.core.predicate="∀us⦂UNIT,um⦂UNIT·us ↦ um∈UH1⇒(us∈dom(OU1)∧um∈dom(OU1)⇒OU1(us)=OU1(um))">
<org.eventb.core.prIdent name="OU1" org.eventb.core.type="ℙ(UNIT×ORG)"/>
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="finite(ACTIVITY)∧finite(ACTION)∧finite(VIEW)∧finite(RESOURCE)">
<org.eventb.core.prIdent name="ACTION" org.eventb.core.type="ℙ(ACTION)"/>
<org.eventb.core.prIdent name="ACTIVITY" org.eventb.core.type="ℙ(ACTIVITY)"/>
<org.eventb.core.prIdent name="RESOURCE" org.eventb.core.type="ℙ(RESOURCE)"/>
<org.eventb.core.prIdent name="VIEW" org.eventb.core.type="ℙ(VIEW)"/>
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<org.eventb.core.prIdent name="EA1" org.eventb.core.type="ℙ(EMPLOYEE×UNIT)"/>
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
<org.eventb.core.prIdent name="UH1" org.eventb.core.type="ℙ(UNIT×UNIT)"/>
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</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="finite(EMPLOYEE)">
<org.eventb.core.prIdent name="EMPLOYEE" org.eventb.core.type="ℙ(EMPLOYEE)"/>
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<org.eventb.core.prIdent name="ACTION" org.eventb.core.type="ℙ(ACTION)"/>
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<org.eventb.core.prPred name="p2" org.eventb.core.predicate="finite(UNIT)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="perms ⇸ COR1≠(∅ ⦂ ℙ(ℙ(PERMISSION×(ORG×ℙ(ℤ×UNIT)))))"/>
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<org.eventb.core.prIdent name="RESOURCE" org.eventb.core.type="ℙ(RESOURCE)"/>
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</org.eventb.core.prPred>
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</org.eventb.core.prProof>
<org.eventb.core.prProof name="Add_Unit_Hierarchy/inv2/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="coc,i" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="ORG,UNIT">
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<org.eventb.theory.core.scDirectOperatorDefinition name="(" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#(|org.eventb.theory.core.directOperatorDefinition#(" org.eventb.theory.core.formula="{n⦂ℤ,f⦂ℙ(ℤ×A)·n∈ℕ∧f∈1 ‥ n → a ∣ f}"/>
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<org.eventb.theory.core.scDirectOperatorDefinition name="(" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#)|org.eventb.theory.core.directOperatorDefinition#(" org.eventb.theory.core.formula="card(s)"/>
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<org.eventb.theory.core.scNewOperatorDefinition name="emptySeq" org.eventb.core.label="emptySeq" org.eventb.core.predicate="⊤" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#5" org.eventb.theory.core.associative="false" org.eventb.theory.core.commutative="false" org.eventb.theory.core.formulaType="true" org.eventb.theory.core.groupID="org.eventb.core.ast.atomicExpr" org.eventb.theory.core.hasError="false" org.eventb.theory.core.notationType="PREFIX" org.eventb.theory.core.type="ℙ(A)" org.eventb.theory.core.wd="⊤">
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<org.eventb.theory.core.scDirectOperatorDefinition name=")" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#,|org.eventb.theory.core.directOperatorDefinition#)" org.eventb.theory.core.formula="λi⦂ℤ·i∈1 ‥ card(s) − 1 ∣ s(i+1)"/>
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<org.eventb.theory.core.scOperatorArgument name="e" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#.|org.eventb.theory.core.operatorArgument#(" org.eventb.core.type="A"/>
<org.eventb.theory.core.scDirectOperatorDefinition name=")" org.eventb.core.source="/CoR/Seq.tuf|org.eventb.theory.core.theoryRoot#Seq|org.eventb.theory.core.newOperatorDefinition#.|org.eventb.theory.core.directOperatorDefinition#)" org.eventb.theory.core.formula="s∪{card(s)+1 ↦ e}"/>
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