# HG changeset patch # User Yasutaka Higa # Date 1400651092 -32400 # Node ID 6b1230883bfa7cd81c01f4c9475ce05f1d1d128e # Parent 7138e79615b33deefe34b1f2e754bd424597db97 mini fixes diff -r 7138e79615b3 -r 6b1230883bfa int.agda --- a/int.agda Wed May 21 14:41:45 2014 +0900 +++ b/int.agda Wed May 21 14:44:52 2014 +0900 @@ -8,9 +8,9 @@ n + O = n n + (S m) = S (n + m) -plus-one : (n m : Int) -> (S n) + m ≡ S (n + m) -plus-one n O = sym refl -plus-one n (S m) = cong S (plus-one n m) +left-increment : (n m : Int) -> (S n) + m ≡ S (n + m) +left-increment n O = refl +left-increment n (S m) = cong S (left-increment n m) double : Int -> Int double O = O @@ -24,11 +24,11 @@ (S n) + (S m) ≡⟨ refl ⟩ S ((S n) + m) - ≡⟨ cong S (plus-one n m)⟩ + ≡⟨ cong S (left-increment n m)⟩ S (S (n + m)) ≡⟨ cong (\x -> S (S x)) (sum-sym n m) ⟩ S (S (m + n)) - ≡⟨ sym (cong S (plus-one m n)) ⟩ + ≡⟨ sym (cong S (left-increment m n)) ⟩ S ((S m) + n) ≡⟨ refl ⟩ (S m) + (S n)