Mercurial > hg > Members > atton > agda > systemT
diff int.agda @ 5:a3cf5cb2b7d3
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 |
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--- a/int.agda Wed May 21 14:44:52 2014 +0900 +++ b/int.agda Wed May 21 14:52:44 2014 +0900 @@ -33,3 +33,13 @@ ≡⟨ refl ⟩ (S m) + (S n) ∎ + +sum-assoc : (x y z : Int) -> x + (y + z) ≡ (x + y) + z +sum-assoc O O O = refl +sum-assoc O O (S z) = cong S (sum-assoc O O z) +sum-assoc O (S y) O = refl +sum-assoc O (S y) (S z) = cong S (sum-assoc O (S y) z) +sum-assoc (S x) O O = refl +sum-assoc (S x) O (S z) = cong S (sum-assoc (S x) O z) +sum-assoc (S x) (S y) O = refl +sum-assoc (S x) (S y) (S z) = cong S (sum-assoc (S x) (S y) z)