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Lots of refactoring towards partially-ordered ring R (#109)

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Patrick Stevens
2020-04-10 19:00:57 +01:00
committed by GitHub
parent 1cff95c652
commit 412edaf4c7
19 changed files with 1015 additions and 778 deletions
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12
LogicalFormulae.agda
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@@ -32,6 +32,12 @@ record _&&_ {a b} (A : Set a) (B : Set b) : Set (a ⊔ b) where
fst : A
snd : B
equalityLeft : {a b : _} {A : Set a} {B : Set b} {x1 x2 : A && B} → (x1 ≡ x2) → _&&_.fst x1 ≡ _&&_.fst x2
equalityLeft {x1 = a ,, _} {.a ,, _} refl = refl
equalityRight : {a b : _} {A : Set a} {B : Set b} {x1 x2 : A && B} → (x1 ≡ x2) → _&&_.snd x1 ≡ _&&_.snd x2
equalityRight {x1 = _ ,, a} {_ ,, .a} refl = refl
infix 15 _&_&_
record _&_&_ {a b c} (A : Set a) (B : Set b) (C : Set c) : Set (a ⊔ b ⊔ c) where
field
@@ -77,9 +83,9 @@ orIsAssociative (inl (inl x)) = inl x
orIsAssociative (inl (inr x)) = inr (inl x)
orIsAssociative (inr x) = inr (inr x)
leqConstructive : {n : _} → {p : Set n} → (p || (p → False)) → (((p → False) → False) → p)
leqConstructive (inl p) = λ _ → p
leqConstructive (inr notP) = λ negnegP → exFalso (negnegP notP)
lemConstructive : {n : _} → {p : Set n} → (p || (p → False)) → (((p → False) → False) → p)
lemConstructive (inl p) = λ _ → p
lemConstructive (inr notP) = λ negnegP → exFalso (negnegP notP)
lemConverse : {n : _} → {p : Set n} → p → ((p → False) → False)
lemConverse p = λ notP → notP p