Mercurial > hg > Members > atton > agda > systemT

comparison int.agda @ 5:a3cf5cb2b7d3

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Auto proof sum-assoc
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Wed, 21 May 2014 14:52:44 +0900
parents 6b1230883bfa
children db4c6d435f23
comparison
equal deleted inserted replaced
4:6b1230883bfa 5:a3cf5cb2b7d3
31 ≡⟨ sym (cong S (left-increment m n)) ⟩ 31 ≡⟨ sym (cong S (left-increment m n)) ⟩
32 S ((S m) + n) 32 S ((S m) + n)
33 ≡⟨ refl ⟩ 33 ≡⟨ refl ⟩
34 (S m) + (S n) 34 (S m) + (S n)
35 ∎ 35 ∎
36
37 sum-assoc : (x y z : Int) -> x + (y + z) ≡ (x + y) + z
38 sum-assoc O O O = refl
39 sum-assoc O O (S z) = cong S (sum-assoc O O z)
40 sum-assoc O (S y) O = refl
41 sum-assoc O (S y) (S z) = cong S (sum-assoc O (S y) z)
42 sum-assoc (S x) O O = refl
43 sum-assoc (S x) O (S z) = cong S (sum-assoc (S x) O z)
44 sum-assoc (S x) (S y) O = refl
45 sum-assoc (S x) (S y) (S z) = cong S (sum-assoc (S x) (S y) z)