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changeset 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
files int.agda
diffstat 1 files changed, 10 insertions(+), 0 deletions(-) [+]
line wrap: on
line diff
--- 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)