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author | 2006-11-21 21:38:49 +0000 | |
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committer | 2006-11-21 21:38:49 +0000 | |
commit | 70b9be8acc1d1ada178a95c1cd4013506e9d0d1b (patch) | |
tree | f672a286d962cc67c95874b3b60402fc957870b6 /theories/Bool/Zerob.v | |
parent | a5bd4e097a94cc4f863bf4d4bcc5ce592c30ba47 (diff) | |
parent | 208a0f7bfa5249f9795e6e225f309cbe715c0fad (diff) |
Merge commit 'upstream/8.1.gamma' into 8.1
Diffstat (limited to 'theories/Bool/Zerob.v')
-rw-r--r-- | theories/Bool/Zerob.v | 18 |
1 files changed, 11 insertions, 7 deletions
diff --git a/theories/Bool/Zerob.v b/theories/Bool/Zerob.v index c9abf94a..fe656777 100644 --- a/theories/Bool/Zerob.v +++ b/theories/Bool/Zerob.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Zerob.v 8642 2006-03-17 10:09:02Z notin $ i*) +(*i $Id: Zerob.v 9245 2006-10-17 12:53:34Z notin $ i*) Require Import Arith. Require Import Bool. @@ -15,24 +15,28 @@ Open Local Scope nat_scope. Definition zerob (n:nat) : bool := match n with - | O => true - | S _ => false + | O => true + | S _ => false end. Lemma zerob_true_intro : forall n:nat, n = 0 -> zerob n = true. -destruct n; [ trivial with bool | inversion 1 ]. +Proof. + destruct n; [ trivial with bool | inversion 1 ]. Qed. Hint Resolve zerob_true_intro: bool. Lemma zerob_true_elim : forall n:nat, zerob n = true -> n = 0. -destruct n; [ trivial with bool | inversion 1 ]. +Proof. + destruct n; [ trivial with bool | inversion 1 ]. Qed. Lemma zerob_false_intro : forall n:nat, n <> 0 -> zerob n = false. -destruct n; [ destruct 1; auto with bool | trivial with bool ]. +Proof. + destruct n; [ destruct 1; auto with bool | trivial with bool ]. Qed. Hint Resolve zerob_false_intro: bool. Lemma zerob_false_elim : forall n:nat, zerob n = false -> n <> 0. -destruct n; [ intro H; inversion H | auto with bool ]. +Proof. + destruct n; [ inversion 1 | auto with bool ]. Qed.
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