diff options
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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