diff options
Diffstat (limited to 'theories/Numbers/Natural/Abstract/NBase.v')
| -rw-r--r-- | theories/Numbers/Natural/Abstract/NBase.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Numbers/Natural/Abstract/NBase.v b/theories/Numbers/Natural/Abstract/NBase.v index 3e4032b5..85e2c2ab 100644 --- a/theories/Numbers/Natural/Abstract/NBase.v +++ b/theories/Numbers/Natural/Abstract/NBase.v @@ -8,7 +8,7 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id: NBase.v 11040 2008-06-03 00:04:16Z letouzey $ i*) +(*i $Id: NBase.v 11674 2008-12-12 19:48:40Z letouzey $ i*) Require Export Decidable. Require Export NAxioms. @@ -48,14 +48,14 @@ 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. +Theorem Neq_sym : 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. +Theorem neq_sym : forall n m : N, n ~= m -> m ~= n. +Proof NZneq_sym. Theorem succ_inj : forall n1 n2 : N, S n1 == S n2 -> n1 == n2. Proof NZsucc_inj. @@ -111,7 +111,7 @@ Qed. Theorem neq_0_succ : forall n : N, 0 ~= S n. Proof. -intro n; apply neq_symm; apply neq_succ_0. +intro n; apply neq_sym; apply neq_succ_0. Qed. (* Next, we show that all numbers are nonnegative and recover regular induction |