diff options
author | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-11-29 17:28:49 +0000 |
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committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-11-29 17:28:49 +0000 |
commit | 9a6e3fe764dc2543dfa94de20fe5eec42d6be705 (patch) | |
tree | 77c0021911e3696a8c98e35a51840800db4be2a9 /theories/Arith/Peano_dec.v | |
parent | 9058fb97426307536f56c3e7447be2f70798e081 (diff) |
Remplacement des fichiers .v ancienne syntaxe de theories, contrib et states par les fichiers nouvelle syntaxe
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5027 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Peano_dec.v')
-rwxr-xr-x | theories/Arith/Peano_dec.v | 26 |
1 files changed, 12 insertions, 14 deletions
diff --git a/theories/Arith/Peano_dec.v b/theories/Arith/Peano_dec.v index 96a8523f9..4d657d060 100755 --- a/theories/Arith/Peano_dec.v +++ b/theories/Arith/Peano_dec.v @@ -8,29 +8,27 @@ (*i $Id$ i*) -Require Decidable. +Require Import Decidable. -V7only [Import nat_scope.]. Open Local Scope nat_scope. -Implicit Variables Type m,n,x,y:nat. +Implicit Types m n x y : nat. -Theorem O_or_S : (n:nat)({m:nat|(S m)=n})+{O=n}. +Theorem O_or_S : forall n, {m : nat | S m = n} + {0 = n}. Proof. -NewInduction n. -Auto. -Left; Exists n; Auto. +induction n. +auto. +left; exists n; auto. Defined. -Theorem eq_nat_dec : (n,m:nat){n=m}+{~(n=m)}. +Theorem eq_nat_dec : forall n m, {n = m} + {n <> m}. Proof. -NewInduction n; NewInduction m; Auto. -Elim (IHn m); Auto. +induction n; induction m; auto. +elim (IHn m); auto. Defined. -Hints Resolve O_or_S eq_nat_dec : arith. +Hint Resolve O_or_S eq_nat_dec: arith. -Theorem dec_eq_nat:(x,y:nat)(decidable (x=y)). -Intros x y; Unfold decidable; Elim (eq_nat_dec x y); Auto with 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. Defined. - |