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m5_semesters.bpr
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m5_semesters.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/inv51/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="PROGRAMME">
<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=""/>
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<org.eventb.core.prIdent name="year" org.eventb.core.type="ℙ(ℤ)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(PROGRAMME×ℤ))∈(∅ ⦂ ℙ(PROGRAMME)) → year"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prProof name="INITIALISATION/inv52/INV" org.eventb.core.confidence="1000" org.eventb.core.prFresh="" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="" org.eventb.core.prSets="MODULE">
<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">
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="semester" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="⊤"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="(∅ ⦂ ℙ(MODULE×ℤ))∈(∅ ⦂ ℙ(MODULE)) → semester"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.trueGoal"/>
<org.eventb.core.prReas name="r0" org.eventb.core.prRID="org.eventb.core.seqprover.autoRewritesL4:0"/>
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<org.eventb.core.prProof name="create_module/inv52/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,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33" org.eventb.core.prSets="MODULE,M_OUTCOME,PROGRAMME,P_OUTCOME,USER">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<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="p13,p33,p16,p20,p21,p28,p7,p3,p26,p25,p17,p23,p6,p30,p24,p10,p8,p12,p29,p11,p14,p4,p5,p9,p19,p31,p1,p15,p27,p22,p2,p32,p34">
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="administrators" org.eventb.core.type="ℙ(PROGRAMME×USER)"/>
<org.eventb.core.prIdent name="c" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="contains_module" org.eventb.core.type="ℙ(PROGRAMME×MODULE)"/>
<org.eventb.core.prIdent name="credits" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="credits_awarded" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="logged_in" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MODULE"/>
<org.eventb.core.prIdent name="module_leader" org.eventb.core.type="ℙ(MODULE×USER)"/>
<org.eventb.core.prIdent name="module_outcomes" org.eventb.core.type="ℙ(MODULE×M_OUTCOME)"/>
<org.eventb.core.prIdent name="module_semester" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="module_year" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="modules" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="outcome_mapping" org.eventb.core.type="ℙ(MODULE×M_OUTCOME×(PROGRAMME×P_OUTCOME))"/>
<org.eventb.core.prIdent name="prerequisites" org.eventb.core.type="ℙ(MODULE×MODULE)"/>
<org.eventb.core.prIdent name="programme_duration" org.eventb.core.type="ℙ(PROGRAMME×ℤ)"/>
<org.eventb.core.prIdent name="programme_leader" org.eventb.core.type="ℙ(PROGRAMME×USER)"/>
<org.eventb.core.prIdent name="programme_outcomes" org.eventb.core.type="ℙ(PROGRAMME×P_OUTCOME)"/>
<org.eventb.core.prIdent name="programmes" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="published" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="s" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="semester" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="sum" org.eventb.core.type="ℙ(ℙ(MODULE×ℤ)×ℤ)"/>
<org.eventb.core.prIdent name="u" org.eventb.core.type="USER"/>
<org.eventb.core.prIdent name="y" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="year" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂MODULE,m2⦂MODULE·{m1,m2}⊆modules∧m2∈prerequisites[{m1}]∧module_year(m1)=module_year(m2)⇒module_semester(m1)>module_semester(m2)"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="registered⊆USER"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="s∈semester"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="year={1,2,3,4}"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀p⦂PROGRAMME,m⦂MODULE·p∈published∧m∈contains_module[{p}]⇒prerequisites[{m}]⊆contains_module[{p}]"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="programme_duration∈programmes → year"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="contains_module∈programmes ↔ modules"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="semester={1,2}"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="programme_outcomes∈programmes ↔ P_OUTCOME"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="module_semester∈modules → semester"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="credits_awarded∈MODULE ⇸ credits"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂MODULE·m∈dom(dom(outcome_mapping))⇒dom(ran(({m} ◁ dom(outcome_mapping)) ◁ outcome_mapping))⊆contains_module∼[{m}]"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="module_outcomes∈modules ↔ M_OUTCOME"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="credits={15,30,45,60}"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="prerequisites∈modules ↔ modules"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀p⦂PROGRAMME,y⦂ℤ,s⦂ℤ·p∈published∧s∈semester∧y∈year⇒sum((contains_module[{p}]∩module_year∼[{y}]∩module_semester∼[{s}]) ◁ credits_awarded)≥30"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="sum(∅ ⦂ ℙ(MODULE×ℤ))=0"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="administrators∈programmes ↔ registered"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="m∉modules"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="module_year∈modules → year"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="(∅ ⦂ ℙ(MODULE×ℤ))∈dom(sum)"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="module_semester{m ↦ s}∈modules∪{m} → semester"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="sum∈ℙ(MODULE × ℤ) ⇸ ℤ"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="c∈credits"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="published⊆programmes"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="programmes⊆PROGRAMME"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="credits_awarded∈modules → credits"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="programme_leader∈programmes → registered"/>
<org.eventb.core.prPred name="p38" org.eventb.core.predicate="m∈MODULE"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="logged_in⊆registered"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="u∈logged_in"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="¬m∈modules"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="∀f⦂ℙ(MODULE×ℤ),m⦂MODULE·f∈MODULE ⇸ credits∧m∈dom(f)⇒sum(f)=sum({m} ⩤ f)+f(m)"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="outcome_mapping∈module_outcomes ↔ programme_outcomes"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="module_leader∈modules → registered"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="∀m1⦂MODULE,m2⦂MODULE·{m1,m2}⊆modules∧m2∈prerequisites[{m1}]⇒module_year(m1)≥module_year(m2)"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="y∈year"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="sum∈(MODULE ↔ credits) → ℕ"/>
<org.eventb.core.prPred name="p37" org.eventb.core.predicate="modules⊆MODULE"/>
<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.typeRewrites:1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="delete_module/inv52/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" org.eventb.core.prSets="MODULE,PROGRAMME,USER">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="REWRITE0" org.eventb.core.prHidden="p6" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p7"/>
<org.eventb.core.prHypAction name="REWRITE1" org.eventb.core.prHidden="p4" org.eventb.core.prHyps="" org.eventb.core.prInfHyps="p8"/>
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<org.eventb.core.prHypAction name="HIDE0" org.eventb.core.prHyps="p9"/>
<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p10"/>
<org.eventb.core.prHypAction name="HIDE2" org.eventb.core.prHyps="p11"/>
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<org.eventb.core.prHypAction name="FORWARD_INF0" org.eventb.core.prHyps="p3" org.eventb.core.prInfHyps="p12"/>
<org.eventb.core.prHypAction name="DESELECT1" org.eventb.core.prHyps="p3"/>
<org.eventb.core.prRule name="r3" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="PP" org.eventb.core.prGoal="p0" org.eventb.core.prHyps="p1,p5,p2,p7,p8,p12">
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</org.eventb.core.prRule>
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</org.eventb.core.prRule>
<org.eventb.core.prIdent name="contains_module" org.eventb.core.type="ℙ(PROGRAMME×MODULE)"/>
<org.eventb.core.prIdent name="logged_in" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="m" org.eventb.core.type="MODULE"/>
<org.eventb.core.prIdent name="module_leader" org.eventb.core.type="ℙ(MODULE×USER)"/>
<org.eventb.core.prIdent name="module_semester" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="modules" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="prerequisites" org.eventb.core.type="ℙ(MODULE×MODULE)"/>
<org.eventb.core.prIdent name="semester" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="u" org.eventb.core.type="USER"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="module_leader(m)=u"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="registered⊆USER">
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
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<org.eventb.core.prPred name="p0" org.eventb.core.predicate="{m} ⩤ module_semester∈modules ∖ {m} → semester"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="m∉ran(prerequisites)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="¬m∈ran(contains_module)"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="¬m∈ran(prerequisites)"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="module_leader(m)∈logged_in"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="programmes⊆PROGRAMME">
<org.eventb.core.prIdent name="programmes" org.eventb.core.type="ℙ(PROGRAMME)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="module_semester∈modules → semester"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="u∈logged_in"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="m∈modules"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="m∉ran(contains_module)"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="modules⊆MODULE"/>
<org.eventb.core.prReas name="r3" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalPP:1"/>
<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.he:1"/>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="create_programme/inv51/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,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31" org.eventb.core.prSets="MODULE,M_OUTCOME,PROGRAMME,P_OUTCOME,USER">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="HIDE1" org.eventb.core.prHyps="p34"/>
<org.eventb.core.prHypAction name="HIDE2" org.eventb.core.prHyps="p35"/>
<org.eventb.core.prHypAction name="HIDE3" org.eventb.core.prHyps="p36"/>
<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="p13,p31,p16,p19,p20,p26,p7,p3,p24,p23,p17,p21,p6,p28,p22,p10,p8,p12,p27,p11,p14,p4,p5,p9,p18,p29,p1,p15,p25,p2,p32">
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</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prIdent name="administrators" org.eventb.core.type="ℙ(PROGRAMME×USER)"/>
<org.eventb.core.prIdent name="contains_module" org.eventb.core.type="ℙ(PROGRAMME×MODULE)"/>
<org.eventb.core.prIdent name="credits" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="credits_awarded" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="d" org.eventb.core.type="ℤ"/>
<org.eventb.core.prIdent name="logged_in" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="module_leader" org.eventb.core.type="ℙ(MODULE×USER)"/>
<org.eventb.core.prIdent name="module_outcomes" org.eventb.core.type="ℙ(MODULE×M_OUTCOME)"/>
<org.eventb.core.prIdent name="module_semester" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="module_year" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="modules" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="outcome_mapping" org.eventb.core.type="ℙ(MODULE×M_OUTCOME×(PROGRAMME×P_OUTCOME))"/>
<org.eventb.core.prIdent name="p" org.eventb.core.type="PROGRAMME"/>
<org.eventb.core.prIdent name="prerequisites" org.eventb.core.type="ℙ(MODULE×MODULE)"/>
<org.eventb.core.prIdent name="programme_duration" org.eventb.core.type="ℙ(PROGRAMME×ℤ)"/>
<org.eventb.core.prIdent name="programme_leader" org.eventb.core.type="ℙ(PROGRAMME×USER)"/>
<org.eventb.core.prIdent name="programme_outcomes" org.eventb.core.type="ℙ(PROGRAMME×P_OUTCOME)"/>
<org.eventb.core.prIdent name="programmes" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="published" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="semester" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prIdent name="sum" org.eventb.core.type="ℙ(ℙ(MODULE×ℤ)×ℤ)"/>
<org.eventb.core.prIdent name="u" org.eventb.core.type="USER"/>
<org.eventb.core.prIdent name="year" org.eventb.core.type="ℙ(ℤ)"/>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂MODULE,m2⦂MODULE·{m1,m2}⊆modules∧m2∈prerequisites[{m1}]∧module_year(m1)=module_year(m2)⇒module_semester(m1)>module_semester(m2)"/>
<org.eventb.core.prPred name="p33" org.eventb.core.predicate="registered⊆USER"/>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="d∈year"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="year={1,2,3,4}"/>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="∀p⦂PROGRAMME,m⦂MODULE·p∈published∧m∈contains_module[{p}]⇒prerequisites[{m}]⊆contains_module[{p}]"/>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="programme_duration∈programmes → year"/>
<org.eventb.core.prPred name="p36" org.eventb.core.predicate="p∈PROGRAMME"/>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="contains_module∈programmes ↔ modules"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="semester={1,2}"/>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="programme_outcomes∈programmes ↔ P_OUTCOME"/>
<org.eventb.core.prPred name="p9" org.eventb.core.predicate="module_semester∈modules → semester"/>
<org.eventb.core.prPred name="p10" org.eventb.core.predicate="credits_awarded∈MODULE ⇸ credits"/>
<org.eventb.core.prPred name="p11" org.eventb.core.predicate="∀m⦂MODULE·m∈dom(dom(outcome_mapping))⇒dom(ran(({m} ◁ dom(outcome_mapping)) ◁ outcome_mapping))⊆contains_module∼[{m}]"/>
<org.eventb.core.prPred name="p12" org.eventb.core.predicate="module_outcomes∈modules ↔ M_OUTCOME"/>
<org.eventb.core.prPred name="p13" org.eventb.core.predicate="credits={15,30,45,60}"/>
<org.eventb.core.prPred name="p14" org.eventb.core.predicate="prerequisites∈modules ↔ modules"/>
<org.eventb.core.prPred name="p15" org.eventb.core.predicate="∀p⦂PROGRAMME,y⦂ℤ,s⦂ℤ·p∈published∧s∈semester∧y∈year⇒sum((contains_module[{p}]∩module_year∼[{y}]∩module_semester∼[{s}]) ◁ credits_awarded)≥30"/>
<org.eventb.core.prPred name="p16" org.eventb.core.predicate="sum(∅ ⦂ ℙ(MODULE×ℤ))=0"/>
<org.eventb.core.prPred name="p17" org.eventb.core.predicate="administrators∈programmes ↔ registered"/>
<org.eventb.core.prPred name="p18" org.eventb.core.predicate="module_year∈modules → year"/>
<org.eventb.core.prPred name="p19" org.eventb.core.predicate="(∅ ⦂ ℙ(MODULE×ℤ))∈dom(sum)"/>
<org.eventb.core.prPred name="p20" org.eventb.core.predicate="sum∈ℙ(MODULE × ℤ) ⇸ ℤ"/>
<org.eventb.core.prPred name="p21" org.eventb.core.predicate="published⊆programmes"/>
<org.eventb.core.prPred name="p34" org.eventb.core.predicate="programmes⊆PROGRAMME"/>
<org.eventb.core.prPred name="p22" org.eventb.core.predicate="credits_awarded∈modules → credits"/>
<org.eventb.core.prPred name="p23" org.eventb.core.predicate="programme_leader∈programmes → registered"/>
<org.eventb.core.prPred name="p24" org.eventb.core.predicate="logged_in⊆registered"/>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="programme_duration{p ↦ d}∈programmes∪{p} → year"/>
<org.eventb.core.prPred name="p25" org.eventb.core.predicate="u∈logged_in"/>
<org.eventb.core.prPred name="p26" org.eventb.core.predicate="∀f⦂ℙ(MODULE×ℤ),m⦂MODULE·f∈MODULE ⇸ credits∧m∈dom(f)⇒sum(f)=sum({m} ⩤ f)+f(m)"/>
<org.eventb.core.prPred name="p27" org.eventb.core.predicate="outcome_mapping∈module_outcomes ↔ programme_outcomes"/>
<org.eventb.core.prPred name="p28" org.eventb.core.predicate="module_leader∈modules → registered"/>
<org.eventb.core.prPred name="p29" org.eventb.core.predicate="∀m1⦂MODULE,m2⦂MODULE·{m1,m2}⊆modules∧m2∈prerequisites[{m1}]⇒module_year(m1)≥module_year(m2)"/>
<org.eventb.core.prPred name="p30" org.eventb.core.predicate="p∉programmes"/>
<org.eventb.core.prPred name="p31" org.eventb.core.predicate="sum∈(MODULE ↔ credits) → ℕ"/>
<org.eventb.core.prPred name="p32" org.eventb.core.predicate="¬p∈programmes"/>
<org.eventb.core.prPred name="p35" org.eventb.core.predicate="modules⊆MODULE"/>
<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.typeRewrites:1"/>
<org.eventb.core.prReas name="r2" org.eventb.core.prRID="com.clearsy.atelierb.provers.core.externalML:1"/>
</org.eventb.core.prProof>
<org.eventb.core.prProof name="create_programme/inv52/INV" org.eventb.core.confidence="0" org.eventb.core.prFresh="" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="REWRITE1" 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.prHypAction name="HIDE2" org.eventb.core.prHyps="p6"/>
<org.eventb.core.prHypAction name="HIDE3" org.eventb.core.prHyps="p7"/>
<org.eventb.core.prHypAction name="HIDE4" org.eventb.core.prHyps="p8"/>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
</org.eventb.core.prAnte>
</org.eventb.core.prRule>
<org.eventb.core.prPred name="p4" org.eventb.core.predicate="registered⊆USER">
<org.eventb.core.prIdent name="USER" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p1" org.eventb.core.predicate="∀m1⦂MODULE,m2⦂MODULE·m1∈modules∧m2∈modules∧¬m1=m2∧m2∈prerequisites[{m1}]⇒contains_module∼[{m1}]⊆contains_module∼[{m2}]">
<org.eventb.core.prIdent name="MODULE" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="PROGRAMME" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="contains_module" org.eventb.core.type="ℙ(PROGRAMME×MODULE)"/>
<org.eventb.core.prIdent name="modules" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="prerequisites" org.eventb.core.type="ℙ(MODULE×MODULE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="mapped∈M_OUTCOME ↔ P_OUTCOME">
<org.eventb.core.prIdent name="M_OUTCOME" org.eventb.core.type="ℙ(M_OUTCOME)"/>
<org.eventb.core.prIdent name="P_OUTCOME" org.eventb.core.type="ℙ(P_OUTCOME)"/>
<org.eventb.core.prIdent name="mapped" org.eventb.core.type="ℙ(M_OUTCOME×P_OUTCOME)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="∀m1⦂MODULE,m2⦂MODULE·m1∈modules∧m2∈modules∧m1≠m2∧m2∈prerequisites[{m1}]⇒contains_module∼[{m1}]⊆contains_module∼[{m2}]">
<org.eventb.core.prIdent name="MODULE" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="PROGRAMME" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="contains_module" org.eventb.core.type="ℙ(PROGRAMME×MODULE)"/>
<org.eventb.core.prIdent name="modules" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="prerequisites" org.eventb.core.type="ℙ(MODULE×MODULE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p2" org.eventb.core.predicate="p∉programmes">
<org.eventb.core.prIdent name="PROGRAMME" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="p" org.eventb.core.type="PROGRAMME"/>
<org.eventb.core.prIdent name="programmes" org.eventb.core.type="ℙ(PROGRAMME)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p8" org.eventb.core.predicate="p∈PROGRAMME">
<org.eventb.core.prIdent name="PROGRAMME" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="p" org.eventb.core.type="PROGRAMME"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p5" org.eventb.core.predicate="programmes⊆PROGRAMME">
<org.eventb.core.prIdent name="PROGRAMME" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="programmes" org.eventb.core.type="ℙ(PROGRAMME)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="¬p∈programmes">
<org.eventb.core.prIdent name="PROGRAMME" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prIdent name="p" org.eventb.core.type="PROGRAMME"/>
<org.eventb.core.prIdent name="programmes" org.eventb.core.type="ℙ(PROGRAMME)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p6" org.eventb.core.predicate="modules⊆MODULE">
<org.eventb.core.prIdent name="MODULE" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="modules" org.eventb.core.type="ℙ(MODULE)"/>
</org.eventb.core.prPred>
<org.eventb.core.prReas name="r1" org.eventb.core.prRID="org.eventb.core.seqprover.typeRewrites: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="delete_programme/inv51/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,p21,p22,p23,p24,p25,p26,p27,p28,p29,p30,p31,p32,p33,p34" org.eventb.core.prSets="MODULE,M_OUTCOME,PROGRAMME,P_OUTCOME,USER">
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<org.eventb.core.prRule name="r0" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="simplification rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prRule name="r1" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="type rewrites" org.eventb.core.prHyps="">
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<org.eventb.core.prHypAction name="HIDE2" org.eventb.core.prHyps="p38"/>
<org.eventb.core.prRule name="r2" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="he with programme_leader(p)=u" org.eventb.core.prHyps="p14">
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<org.eventb.core.prIdent name="credits_awarded" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
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<org.eventb.core.prIdent name="module_leader" org.eventb.core.type="ℙ(MODULE×USER)"/>
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<org.eventb.core.prIdent name="module_semester" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
<org.eventb.core.prIdent name="module_year" org.eventb.core.type="ℙ(MODULE×ℤ)"/>
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<org.eventb.core.prIdent name="programme_duration" org.eventb.core.type="ℙ(PROGRAMME×ℤ)"/>
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<org.eventb.core.prIdent name="published" org.eventb.core.type="ℙ(PROGRAMME)"/>
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<org.eventb.core.prIdent name="sum" org.eventb.core.type="ℙ(ℙ(MODULE×ℤ)×ℤ)"/>
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<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="p12">
<org.eventb.core.prRule name="r5" org.eventb.core.confidence="1000" org.eventb.core.prDisplay="functional goal" org.eventb.core.prGoal="p12" org.eventb.core.prHyps="p2"/>
</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="p" org.eventb.core.type="PROGRAMME"/>
<org.eventb.core.prIdent name="programme_duration" org.eventb.core.type="ℙ(PROGRAMME×ℤ)"/>
<org.eventb.core.prIdent name="programmes" org.eventb.core.type="ℙ(PROGRAMME)"/>
<org.eventb.core.prPred name="p7" org.eventb.core.predicate="registered⊆USER">
<org.eventb.core.prIdent name="USER" org.eventb.core.type="ℙ(USER)"/>
<org.eventb.core.prIdent name="registered" org.eventb.core.type="ℙ(USER)"/>
</org.eventb.core.prPred>
<org.eventb.core.prPred name="p0" org.eventb.core.predicate="p∈dom(programme_duration)∧programme_duration∈PROGRAMME ⇸ ℤ"/>
<org.eventb.core.prPred name="p3" org.eventb.core.predicate="∀m1⦂MODULE,m2⦂MODULE·m1∈modules∧m2∈modules∧m1≠m2∧m2∈prerequisites[{m1}]⇒contains_module∼[{m1}]⊆contains_module∼[{m2}]">
<org.eventb.core.prIdent name="MODULE" org.eventb.core.type="ℙ(MODULE)"/>
<org.eventb.core.prIdent name="contains_module" org.eventb.core.type="ℙ(PROGRAMME×MODULE)"/>