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author | 2002-05-07 13:25:57 +0000 | |
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committer | 2002-05-07 13:25:57 +0000 | |
commit | d85c5b3a639da751422e6cd342c075941bd6b43f (patch) | |
tree | d433812b76e7e043c14a7e41e5921f725e151efe /theories/Init | |
parent | 5a6c49f8100da35be59cb7381e55d1fb7c8572e6 (diff) |
lemmes plus_O_n et plus_Sn_m (pour Yves)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2671 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Init')
-rwxr-xr-x | theories/Init/Peano.v | 14 |
1 files changed, 12 insertions, 2 deletions
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v index 53439d6b6..a025d148b 100755 --- a/theories/Init/Peano.v +++ b/theories/Init/Peano.v @@ -88,13 +88,23 @@ Lemma plus_n_O : (n:nat) n=(plus n O). Proof. Induction n ; Simpl ; Auto. Qed. -Hints Resolve plus_n_O : core v62. + +Lemma plus_O_n : (n:nat) (plus O n)=n. +Proof. + Auto. +Qed. +Hints Resolve plus_n_O plus_O_n : core v62. Lemma plus_n_Sm : (n,m:nat) (S (plus n m))=(plus n (S m)). Proof. Intros m n; Elim m; Simpl; Auto. Qed. -Hints Resolve plus_n_Sm : core v62. + +Lemma plus_Sn_m : (n,m:nat)(plus (S n) m)=(S (plus n m)). +Proof. + Auto. +Qed. +Hints Resolve plus_n_Sm plus_Sn_m : core v62. (** Multiplication *) |