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| author | Helmut Grohne <helmut@subdivi.de> | 2013-01-28 12:28:08 +0100 |
|---|---|---|
| committer | Helmut Grohne <helmut@subdivi.de> | 2013-01-28 12:28:08 +0100 |
| commit | a1dc58fcd06028cb968c99a67db4b44bd1abc3d7 (patch) | |
| tree | 2cf2fb32ef675f4b3bba88c26b73b9fd2a23e047 /FinMap.agda | |
| parent | 9c20cf71b1136f7461a8a2062c9c9852518fd707 (diff) | |
| download | bidiragda-a1dc58fcd06028cb968c99a67db4b44bd1abc3d7.tar.gz | |
polish lemmata in FinMap
Diffstat (limited to 'FinMap.agda')
| -rw-r--r-- | FinMap.agda | 14 |
1 files changed, 5 insertions, 9 deletions
diff --git a/FinMap.agda b/FinMap.agda index 8b4103b..7df4f7b 100644 --- a/FinMap.agda +++ b/FinMap.agda @@ -59,8 +59,8 @@ lemma-lookupM-empty zero = refl lemma-lookupM-empty (suc i) = lemma-lookupM-empty i lemma-lookupM-insert : {A : Set} {n : ℕ} → (i : Fin n) → (a : A) → (m : FinMapMaybe n A) → lookupM i (insert i a m) ≡ just a -lemma-lookupM-insert zero _ (_ ∷ _) = refl -lemma-lookupM-insert (suc i) a (_ ∷ xs) = lemma-lookupM-insert i a xs +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 : ℕ} → (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 zero zero a m p = contradiction refl p @@ -72,22 +72,18 @@ just-injective : {A : Set} → {x y : A} → _≡_ {_} {Maybe A} (just x) (just just-injective refl = refl lemma-lookupM-restrict : {A : Set} {n : ℕ} → (i : Fin n) → (f : Fin n → A) → (is : List (Fin n)) → (a : A) → lookupM i (restrict f is) ≡ just a → f i ≡ a -lemma-lookupM-restrict i f [] a p = lemma-just≢nothing p (lemma-lookupM-empty i) +lemma-lookupM-restrict i f [] a p = lemma-just≢nothing p (lemma-lookupM-empty i) lemma-lookupM-restrict i f (i' ∷ is) a p with i ≟ i' lemma-lookupM-restrict i f (.i ∷ is) a p | yes refl = just-injective (begin just (f i) ≡⟨ sym (lemma-lookupM-insert i (f i) (restrict f is)) ⟩ lookupM i (insert i (f i) (restrict f is)) - ≡⟨ refl ⟩ - lookupM i (restrict f (i ∷ is)) ≡⟨ p ⟩ just a ∎) -lemma-lookupM-restrict i f (i' ∷ is) a p | no ¬p2 = lemma-lookupM-restrict i f is a (begin +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) ¬p2 ⟩ + ≡⟨ lemma-lookupM-insert-other i i' (f i') (restrict f is) i≢i' ⟩ lookupM i (insert i' (f i') (restrict f is)) - ≡⟨ refl ⟩ - lookupM i (restrict f (i' ∷ is)) ≡⟨ p ⟩ just a ∎) |