diff options
Diffstat (limited to 'Precond.agda')
| -rw-r--r-- | Precond.agda | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/Precond.agda b/Precond.agda index 31ac04b..ffbe0e7 100644 --- a/Precond.agda +++ b/Precond.agda @@ -88,21 +88,21 @@ assoc-enough′ G {i} s v (h , p) = _ , (begin g = fromFunc (denumerate SourceShapeT s) g′ = delete-many (Shaped.content ViewShapeT (get s′)) g t = enumerate SourceShapeT (|gl₁| i) - wp = lemma-union-delete-fromFunc (lemma-assoc-domain (Shaped.content ViewShapeT (get t)) (Shaped.content ViewShapeT v) h p) + wp = lemma-union-delete-fromFunc (lemma-assoc-domain (Shaped.content ViewShapeT (get t)) (Shaped.content ViewShapeT v) p) data All-different {A : Set} : List A → Set where different-[] : All-different [] different-∷ : {x : A} {xs : List A} → x ∉ xs → All-different xs → All-different (x ∷ xs) -lemma-∉-lookupM-assoc : {m n : ℕ} → (i : Fin n) → (is : Vec (Fin n) m) → (xs : Vec Carrier m) → (h : FinMapMaybe n Carrier) → assoc is xs ≡ just h → (i ∉ toList is) → lookupM i h ≡ nothing -lemma-∉-lookupM-assoc i [] [] .empty refl i∉is = lemma-lookupM-empty i -lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') h ph i∉is with assoc is' xs' | inspect (assoc is') xs' -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 +lemma-∉-lookupM-assoc : {m n : ℕ} → (i : Fin n) → (is : Vec (Fin n) m) → (xs : Vec Carrier m) → {h : FinMapMaybe n Carrier} → assoc is xs ≡ just h → (i ∉ toList is) → lookupM i h ≡ nothing +lemma-∉-lookupM-assoc i [] [] refl i∉is = lemma-lookupM-empty i +lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') ph i∉is with assoc is' xs' | inspect (assoc is') xs' +lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') () i∉is | nothing | [ ph' ] +lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') {h} ph i∉is | just h' | [ ph' ] = begin lookupM i h - ≡⟨ lemma-lookupM-checkInsert-other i i' (i∉is ∘ here) x' h' h ph ⟩ + ≡⟨ lemma-lookupM-checkInsert-other i i' (i∉is ∘ here) x' h' ph ⟩ lookupM i h' - ≡⟨ lemma-∉-lookupM-assoc i is' xs' h' ph' (i∉is ∘ there) ⟩ + ≡⟨ lemma-∉-lookupM-assoc i is' xs' ph' (i∉is ∘ there) ⟩ nothing ∎ different-assoc : {m n : ℕ} → (u : Vec (Fin n) m) → (v : Vec Carrier m) → All-different (toList u) → ∃ λ h → assoc u v ≡ just h @@ -114,5 +114,5 @@ different-assoc (u ∷ us) (v ∷ vs) (different-∷ u∉us diff-us) | h , p' = (assoc us vs >>= checkInsert u v) ≡⟨ cong (flip _>>=_ (checkInsert u v)) p' ⟩ checkInsert u v h - ≡⟨ lemma-checkInsert-new u v h (lemma-∉-lookupM-assoc u us vs h p' u∉us) ⟩ + ≡⟨ lemma-checkInsert-new u v h (lemma-∉-lookupM-assoc u us vs p' u∉us) ⟩ just (insert u v h) ∎) |