diff options
Diffstat (limited to 'theories/Numbers/Natural/Abstract/NBase.v')
| -rw-r--r-- | theories/Numbers/Natural/Abstract/NBase.v | 9 |
1 files changed, 9 insertions, 0 deletions
diff --git a/theories/Numbers/Natural/Abstract/NBase.v b/theories/Numbers/Natural/Abstract/NBase.v index bcef66867..956eca896 100644 --- a/theories/Numbers/Natural/Abstract/NBase.v +++ b/theories/Numbers/Natural/Abstract/NBase.v @@ -45,6 +45,15 @@ Proof NZpred_succ. Theorem pred_0 : P 0 == 0. Proof pred_0. +Theorem Neq_refl : forall n : N, n == n. +Proof (proj1 NZeq_equiv). + +Theorem Neq_symm : forall n m : N, n == m -> m == n. +Proof (proj2 (proj2 NZeq_equiv)). + +Theorem Neq_trans : forall n m p : N, n == m -> m == p -> n == p. +Proof (proj1 (proj2 NZeq_equiv)). + Theorem neq_symm : forall n m : N, n ~= m -> m ~= n. Proof NZneq_symm. |