diff options
Diffstat (limited to 'theories/Arith/Peano_dec.v')
| -rw-r--r-- | theories/Arith/Peano_dec.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/Arith/Peano_dec.v b/theories/Arith/Peano_dec.v index 4aef7dc0..b17021bc 100644 --- a/theories/Arith/Peano_dec.v +++ b/theories/Arith/Peano_dec.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Peano_dec.v 8642 2006-03-17 10:09:02Z notin $ i*) +(*i $Id: Peano_dec.v 9245 2006-10-17 12:53:34Z notin $ i*) Require Import Decidable. @@ -16,19 +16,19 @@ Implicit Types m n x y : nat. Theorem O_or_S : forall n, {m : nat | S m = n} + {0 = n}. Proof. -induction n. -auto. -left; exists n; auto. + induction n. + auto. + left; exists n; auto. Defined. Theorem eq_nat_dec : forall n m, {n = m} + {n <> m}. Proof. -induction n; induction m; auto. -elim (IHn m); auto. + induction n; induction m; auto. + elim (IHn m); auto. Defined. Hint Resolve O_or_S eq_nat_dec: arith. Theorem dec_eq_nat : forall n m, decidable (n = m). -intros x y; unfold decidable in |- *; elim (eq_nat_dec x y); auto with arith. + intros x y; unfold decidable in |- *; elim (eq_nat_dec x y); auto with arith. Defined. |