diff options
Diffstat (limited to 'FinMap.agda')
| -rw-r--r-- | FinMap.agda | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/FinMap.agda b/FinMap.agda index 4fc3e18..c085b24 100644 --- a/FinMap.agda +++ b/FinMap.agda @@ -68,13 +68,13 @@ lemma-lookupM-insert-other zero (suc j) a (x ∷ xs) p = refl lemma-lookupM-insert-other (suc i) zero a (x ∷ xs) p = refl lemma-lookupM-insert-other (suc i) (suc j) a (x ∷ xs) p = lemma-lookupM-insert-other i j a xs (contraposition (cong suc) p) -lemma-from-just : {A : Set} → {x y : A} → _≡_ {_} {Maybe A} (just x) (just y) → x ≡ y -lemma-from-just refl = refl +just-injective : {A : Set} → {x y : A} → _≡_ {_} {Maybe A} (just x) (just y) → x ≡ y +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 (trans (sym 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 = lemma-from-just (begin +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)) |