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Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZBase.v')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZBase.v | 9 |
1 files changed, 9 insertions, 0 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZBase.v b/theories/Numbers/Integer/Abstract/ZBase.v index db5bc99f9..0813a3caa 100644 --- a/theories/Numbers/Integer/Abstract/ZBase.v +++ b/theories/Numbers/Integer/Abstract/ZBase.v @@ -33,6 +33,15 @@ Proof NZpred_wd. Theorem Zpred_succ : forall n : Z, P (S n) == n. Proof NZpred_succ. +Theorem Zeq_refl : forall n : Z, n == n. +Proof (proj1 NZeq_equiv). + +Theorem Zeq_symm : forall n m : Z, n == m -> m == n. +Proof (proj2 (proj2 NZeq_equiv)). + +Theorem Zeq_trans : forall n m p : Z, n == m -> m == p -> n == p. +Proof (proj1 (proj2 NZeq_equiv)). + Theorem Zneq_symm : forall n m : Z, n ~= m -> m ~= n. Proof NZneq_symm. |