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Actually fix the build (#123)

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Patrick Stevens
2020-04-19 07:17:23 +01:00
committed by GitHub
parent 750a77b7d8
commit 3afdc6d45b
1 changed files with 9 additions and 9 deletions
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18
Logic/PropositionalLogicExamples.agda
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@@ -14,10 +14,10 @@ emptySubset : {a : _} (A : Set a) → IsSubset False A
emptySubset A = record { ofElt = λ () }
emptyEntailment : {a b : _} {A : Set a} {P : Propositions A} → Entails (emptySubset (Propositions A)) P → Tautology P
emptyEntailment {a} {b} {A} {P} record { entails = entails } v = entails {v} λ {s} → exFalso s
emptyEntailment {a} {b} {A} {P} entails v = entails {v} λ {s} → exFalso s
emptyEntailment' : {a b : _} {A : Set a} {P : Propositions A} → Tautology P → Entails (emptySubset (Propositions A)) P
Entails.entails (emptyEntailment' isTaut) {v} _ = isTaut v
emptyEntailment' isTaut {v} _ = isTaut v
data TwoElements : Set where
One : TwoElements
@@ -39,13 +39,13 @@ badBool : BoolFalse ≡ BoolTrue → False
badBool ()
semanticEntailmentTransitive : {a : _} {A : Set a} {P Q R : Propositions A} → (p!=q : P ≡ Q → False) → Entails record { ofElt = twoElementSubset } (implies P R)
Entails.entails (semanticEntailmentTransitive {P = P} {Q} {R} p!=q) {v} pr with inspect (Valuation.v v P)
Entails.entails (semanticEntailmentTransitive {P = P} {Q} {R} p!=q) {v} pr | BoolTrue with≡ pT with inspect (Valuation.v v Q)
Entails.entails (semanticEntailmentTransitive {P = P} {Q} {R} p!=q) {v} pr | BoolTrue with≡ pT | BoolTrue with≡ qT with inspect (Valuation.v v R)
Entails.entails (semanticEntailmentTransitive {P = P} {Q} {R} p!=q) {v} pr | BoolTrue with≡ pT | BoolTrue with≡ qT | BoolTrue with≡ rT = Valuation.vImplicationT v rT
Entails.entails (semanticEntailmentTransitive {P = P} {Q} {R} p!=q) {v} pr | BoolTrue with≡ pT | BoolTrue with≡ qT | BoolFalse with≡ rF = exFalso (badBool (transitivity (equalityCommutative (Valuation.vImplicationF v qT rF)) (pr {Two})))
Entails.entails (semanticEntailmentTransitive {P = P} {Q} {R} p!=q) {v} pr | BoolTrue with≡ pT | BoolFalse with≡ qF = exFalso (badBool (transitivity (equalityCommutative (Valuation.vImplicationF v pT qF)) (pr {One})))
Entails.entails (semanticEntailmentTransitive {P = P} {Q} {R} p!=q) {v} pr | BoolFalse with≡ pF = Valuation.vImplicationVacuous v pF
semanticEntailmentTransitive {P = P} {Q} {R} p!=q {v} pr with inspect (Valuation.v v P)
semanticEntailmentTransitive {P = P} {Q} {R} p!=q {v} pr | BoolTrue with≡ pT with inspect (Valuation.v v Q)
semanticEntailmentTransitive {P = P} {Q} {R} p!=q {v} pr | BoolTrue with≡ pT | BoolTrue with≡ qT with inspect (Valuation.v v R)
semanticEntailmentTransitive {P = P} {Q} {R} p!=q {v} pr | BoolTrue with≡ pT | BoolTrue with≡ qT | BoolTrue with≡ rT = Valuation.vImplicationT v rT
semanticEntailmentTransitive {P = P} {Q} {R} p!=q {v} pr | BoolTrue with≡ pT | BoolTrue with≡ qT | BoolFalse with≡ rF = exFalso (badBool (transitivity (equalityCommutative (Valuation.vImplicationF v qT rF)) (pr {Two})))
semanticEntailmentTransitive {P = P} {Q} {R} p!=q {v} pr | BoolTrue with≡ pT | BoolFalse with≡ qF = exFalso (badBool (transitivity (equalityCommutative (Valuation.vImplicationF v pT qF)) (pr {One})))
semanticEntailmentTransitive {P = P} {Q} {R} p!=q {v} pr | BoolFalse with≡ pF = Valuation.vImplicationVacuous v pF
-- Subset {p -> q, q -> r}
pQQR : {a : _} {A : Set a} {P Q R : Propositions A} → TwoElements → Propositions A