diff options
| -rw-r--r-- | CheckInsert.agda | 4 | ||||
| -rw-r--r-- | FinMap.agda | 6 | ||||
| -rw-r--r-- | Precond.agda | 2 |
3 files changed, 6 insertions, 6 deletions
diff --git a/CheckInsert.agda b/CheckInsert.agda index 9dc8a60..52dffc4 100644 --- a/CheckInsert.agda +++ b/CheckInsert.agda @@ -70,7 +70,7 @@ lemma-lookupM-checkInsert i j x y h h' pl ph' | ._ | new _ with i ≟ j lemma-lookupM-checkInsert i .i x y h h' pl ph' | ._ | new pl' | yes refl = contradiction (trans (sym pl) pl') (λ ()) lemma-lookupM-checkInsert i j x y h .(insert j y h) pl refl | ._ | new _ | no i≢j = begin lookupM i (insert j y h) - ≡⟨ sym (lemma-lookupM-insert-other i j y h i≢j) ⟩ + ≡⟨ lemma-lookupM-insert-other i j y h i≢j ⟩ lookupM i h ≡⟨ pl ⟩ just x ∎ @@ -78,7 +78,7 @@ lemma-lookupM-checkInsert i j x y h .(insert j y h) pl refl | ._ | new _ | no iâ lemma-lookupM-checkInsert i j x y h h' pl () | ._ | wrong _ _ _ -lemma-lookupM-checkInsert-other : {n : â„•} → (i j : Fin n) → i ≢ j → (x : Carrier) → (h h' : FinMapMaybe n Carrier) → checkInsert j x h ≡ just h' → lookupM i h ≡ lookupM i h' +lemma-lookupM-checkInsert-other : {n : â„•} → (i j : Fin n) → i ≢ j → (x : Carrier) → (h h' : FinMapMaybe n Carrier) → checkInsert j x h ≡ just h' → lookupM i h' ≡ lookupM i h lemma-lookupM-checkInsert-other i j i≢j x h h' ph' with lookupM j h lemma-lookupM-checkInsert-other i j i≢j x h h' ph' | just y with deq x y lemma-lookupM-checkInsert-other i j i≢j x h .h refl | just y | yes x≈y = refl diff --git a/FinMap.agda b/FinMap.agda index 05b251e..f9572b8 100644 --- a/FinMap.agda +++ b/FinMap.agda @@ -70,7 +70,7 @@ lemma-lookupM-insert : {A : Set} {n : â„•} → (i : Fin n) → (a : A) → (m : lemma-lookupM-insert zero a (x ∷ xs) = refl lemma-lookupM-insert (suc i) a (x ∷ xs) = lemma-lookupM-insert i a xs -lemma-lookupM-insert-other : {A : Set} {n : â„•} → (i j : Fin n) → (a : A) → (m : FinMapMaybe n A) → i ≢ j → lookupM i m ≡ lookupM i (insert j a m) +lemma-lookupM-insert-other : {A : Set} {n : â„•} → (i j : Fin n) → (a : A) → (m : FinMapMaybe n A) → i ≢ j → lookupM i (insert j a m) ≡ lookupM i m lemma-lookupM-insert-other zero zero a m p = contradiction refl p lemma-lookupM-insert-other zero (suc j) a (x ∷ xs) p = refl lemma-lookupM-insert-other (suc i) zero a (x ∷ xs) p = refl @@ -87,7 +87,7 @@ lemma-lookupM-restrict i f (.i ∷ is) a p | yes refl = just-injective (begin just a ∎) lemma-lookupM-restrict i f (i' ∷ is) a p | no i≢i' = lemma-lookupM-restrict i f is a (begin lookupM i (restrict f is) - ≡⟨ lemma-lookupM-insert-other i i' (f i') (restrict f is) i≢i' ⟩ + ≡⟨ sym (lemma-lookupM-insert-other i i' (f i') (restrict f is) i≢i') ⟩ lookupM i (insert i' (f i') (restrict f is)) ≡⟨ p ⟩ just a ∎) @@ -123,7 +123,7 @@ lemma-disjoint-union {n} {m} f t = lemma-tabulate-∘ (lemma-inner t) lemma-inner (.x ∷ ts) x | yes refl = cong (maybe′ just (lookupM x (delete-many (x ∷ ts) (fromFunc f)))) (lemma-lookupM-insert x (f x) (restrict f (toList ts))) lemma-inner (t ∷ ts) x | no ¬p = begin maybe′ just (lookupM x (delete-many (t ∷ ts) (fromFunc f))) (lookupM x (restrict f (toList (t ∷ ts)))) - ≡⟨ cong (maybe′ just (lookupM x (delete-many (t ∷ ts) (fromFunc f)))) (sym (lemma-lookupM-insert-other x t (f t) (restrict f (toList ts)) ¬p)) ⟩ + ≡⟨ cong (maybe′ just (lookupM x (delete-many (t ∷ ts) (fromFunc f)))) (lemma-lookupM-insert-other x t (f t) (restrict f (toList ts)) ¬p) ⟩ maybe′ just (lookupM x (delete-many (t ∷ ts) (fromFunc f))) (lookupM x (restrict f (toList ts))) ≡⟨ cong (flip (maybe′ just) (lookupM x (restrict f (toList ts)))) (lemma-lookupM-delete (delete-many ts (fromFunc f)) ¬p) ⟩ maybe′ just (lookupM x (delete-many ts (fromFunc f))) (lookupM x (restrict f (toList ts))) diff --git a/Precond.agda b/Precond.agda index 85c955c..8d2eab2 100644 --- a/Precond.agda +++ b/Precond.agda @@ -100,7 +100,7 @@ lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') h ph i∉is with assoc is' x lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') h () i∉is | nothing | [ ph' ] lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') h ph i∉is | just h' | [ ph' ] = begin lookupM i h - ≡⟨ sym (lemma-lookupM-checkInsert-other i i' (i∉is ∘ here) x' h' h ph) ⟩ + ≡⟨ lemma-lookupM-checkInsert-other i i' (i∉is ∘ here) x' h' h ph ⟩ lookupM i h' ≡⟨ lemma-∉-lookupM-assoc i is' xs' h' ph' (i∉is ∘ there) ⟩ nothing ∎ |