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m0_users.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="" org.eventb.core.prSets="USER">
<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="p1">
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p1" org.eventb.core.prHyps=""/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(USER))⊆(∅ ⦂ ℙ(USER))"/>
<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.trueGoal"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="register/inv2/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="USER">
<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="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p4"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p5"/>
<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="p1,p3">
<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.prIdent name="logged_in" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="u" org.eventb.core.type="USER"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="registered⊆USER"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="logged_in⊆registered"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="u∉registered"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="logged_in⊆registered∪{u}"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬u∈registered"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="u∈USER"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r2" 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="unregister/inv2/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3" org.eventb.core.prSets="USER">
<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="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p5"/>
<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="p2,p1,p4">
<org.eventb.core.prString name=".arg" org.eventb.core.prSValue="0;1:500"/>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="logged_in" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="u" org.eventb.core.type="USER"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="u∈registered"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="registered⊆USER"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="logged_in⊆registered"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="u∉logged_in"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="logged_in⊆registered ∖ {u}"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬u∈logged_in"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r2" 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="login/inv2/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="USER">
<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="p5">
<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p3" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p4"/>
<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="generalized MP" org.eventb.core.prGoal="p5" org.eventb.core.prHyps="p1,p2">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p6">
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prGoal="p6" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'" org.eventb.core.prGoal="p7">
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="⊤ goal" org.eventb.core.prGoal="p7" 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="logged_in" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="u" org.eventb.core.type="USER"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="⊤∧⊤"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="u∈registered"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="logged_in∪{u}⊆registered"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="logged_in⊆registered"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="u∉logged_in"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="logged_in⊆registered∧u∈registered"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="¬u∈logged_in"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.genMPL3"/>
<org.eventb.core.prReas name="r0" 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="logout/inv2/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p2,p3" org.eventb.core.prSets="USER">
<org.eventb.core.lang name="L"/>
<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
<org.eventb.core.prAnte name="'">
<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p4"/>
<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="p2,p1,p3">
<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="logged_in" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="u" org.eventb.core.type="USER"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="u∈registered"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="registered⊆USER"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="logged_in⊆registered"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="u∈logged_in"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="logged_in ∖ {u}⊆registered"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
</org.eventb.core.prProof>
</org.eventb.core.prFile>