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| author | emakarov | 2007-11-16 20:37:52 +0000 |
|---|---|---|
| committer | emakarov | 2007-11-16 20:37:52 +0000 |
| commit | cb24ec6fd2c79a317f98b7dad426ac3e9bbad56a (patch) | |
| tree | ee7e4b0f0928e3588adcc4d21e0ca8547f7bd379 /theories/Numbers/Integer/Abstract/ZBase.v | |
| parent | d3cf0e074d4b4a3ddc1de4c91a235474eead80aa (diff) | |
Added theorems; created NZPlusOrder from NTimesOrder.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10325 85f007b7-540e-0410-9357-904b9bb8a0f7
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 db5bc99f92..0813a3caae 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. |