diff options
Diffstat (limited to 'Bidir.agda')
| -rw-r--r-- | Bidir.agda | 4 |
1 files changed, 2 insertions, 2 deletions
@@ -63,7 +63,7 @@ lemma-assoc-domain (i' ∷ is') (x' ∷ xs') h () | just h' | [ ph' ] | ._ | _ | lemma-map-lookupM-assoc : {m : ℕ} → (i : Fin m) → (x : Carrier) → (h : FinMapMaybe m Carrier) → (h' : FinMapMaybe m Carrier) → checkInsert i x h' ≡ just h → {n : ℕ} → (js : Vec (Fin m) n) → (toList js) in-domain-of h' → map (flip lookupM h) js ≡ map (flip lookupM h') js lemma-map-lookupM-assoc i x h h' ph [] pj = refl -lemma-map-lookupM-assoc i x h h' ph (j ∷ js) (All._∷_ (x' , pl) pj) = cong₂ _∷_ +lemma-map-lookupM-assoc i x h h' ph (j ∷ js) (Data.List.All._∷_ (x' , pl) pj) = cong₂ _∷_ (trans (lemma-lookupM-checkInsert j i x' x h' h pl ph) (sym pl)) (lemma-map-lookupM-assoc i x h h' ph js pj) @@ -138,7 +138,7 @@ map-just-injective {xs = x ∷ xs'} {ys = .x ∷ ys'} p | refl , p' = cong (_∷ lemma-union-not-used : {m n : ℕ} {A : Set} (h : FinMapMaybe n A) → (h' : FinMap n A) → (is : Vec (Fin n) m) → (toList is) in-domain-of h → map just (map (flip lookup (union h h')) is) ≡ map (flip lookupM h) is lemma-union-not-used h h' [] p = refl -lemma-union-not-used h h' (i ∷ is') (All._∷_ (x , px) p') = cong₂ _∷_ (begin +lemma-union-not-used h h' (i ∷ is') (Data.List.All._∷_ (x , px) p') = cong₂ _∷_ (begin just (lookup i (union h h')) ≡⟨ cong just (lookup∘tabulate (λ j → maybe′ id (lookup j h') (lookupM j h)) i) ⟩ just (maybe′ id (lookup i h') (lookupM i h)) |