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| author | Helmut Grohne <grohne@cs.uni-bonn.de> | 2014-10-17 15:36:45 +0200 |
|---|---|---|
| committer | Helmut Grohne <grohne@cs.uni-bonn.de> | 2014-10-17 15:36:45 +0200 |
| commit | 58bce3d887d1e5fef24254098819dd09e900fb4c (patch) | |
| tree | 97479d42264538ec648fba64b95c4be686dbd447 | |
| parent | 71c4040262bd1c0ac5962425ee4b3bb3b51cc93b (diff) | |
| download | bidiragda-58bce3d887d1e5fef24254098819dd09e900fb4c.tar.gz | |
generalize lemma-union-not-used
| -rw-r--r-- | Bidir.agda | 14 |
1 files changed, 7 insertions, 7 deletions
@@ -162,14 +162,14 @@ lemma-<$>-just : {A B : Set} {f : A → B} {b : B} (ma : Maybe A) → f <$> ma lemma-<$>-just (just x) f<$>ma≡just-b = x , refl lemma-<$>-just nothing () -lemma-union-not-used : {m n n' : ℕ} {A : Set} (h : FinMapMaybe n A) → (h' : FinMapMaybe n' A) → (is : Vec (Fin n) m) → (toList is) in-domain-of h → map (flip lookupM (union h (reshape h' n))) is ≡ map (flip lookupM h) is +lemma-union-not-used : {m n : ℕ} {A : Set} (h h' : FinMapMaybe n A) → (is : Vec (Fin n) m) → (toList is) in-domain-of h → map (flip lookupM (union h h')) is ≡ map (flip lookupM h) is lemma-union-not-used h h' [] p = refl lemma-union-not-used {n = n} h h' (i ∷ is') (Data.List.All._∷_ (x , px) p') = cong₂ _∷_ (begin - lookupM i (union h (reshape h' n)) - ≡⟨ lookup∘tabulate (λ j → maybe′ just (lookupM j (reshape h' n)) (lookupM j h)) i ⟩ - maybe′ just (lookupM i (reshape h' n)) (lookupM i h) - ≡⟨ cong (maybe′ just (lookupM i (reshape h' n))) px ⟩ - maybe′ just (lookupM i (reshape h' n)) (just x) + lookupM i (union h h') + ≡⟨ lookup∘tabulate (λ j → maybe′ just (lookupM j h') (lookupM j h)) i ⟩ + maybe′ just (lookupM i h') (lookupM i h) + ≡⟨ cong (maybe′ just (lookupM i h')) px ⟩ + maybe′ just (lookupM i h') (just x) ≡⟨ sym px ⟩ lookupM i h ∎) (lemma-union-not-used h h' is' p') @@ -281,7 +281,7 @@ theorem-2 G {i} j s v u p | h′ , ph′ | h , ph = refl , (begin⟨ VecISetoid content (fmapV (flip lookupM (h↦h′ h)) (get t)) ≡⟨ Shaped.fmap-content ViewShapeT (flip lookupM (h↦h′ h)) (get t) ⟩ map (flip lookupM (h↦h′ h)) (content (get t)) - ≡⟨ lemma-union-not-used h g′ (content (get t)) (lemma-assoc-domain (content (get t)) (content v) h ph) ⟩ + ≡⟨ lemma-union-not-used h (reshape g′ (Shaped.arity SourceShapeT (|gl₁| j))) (content (get t)) (lemma-assoc-domain (content (get t)) (content v) h ph) ⟩ map (flip lookupM h) (content (get t)) ≈⟨ lemma-2 (content (get t)) (content v) h ph ⟩ map just (content v) |