diff options
Diffstat (limited to 'theories/Arith/EqNat.v')
| -rw-r--r-- | theories/Arith/EqNat.v | 12 |
1 files changed, 11 insertions, 1 deletions
diff --git a/theories/Arith/EqNat.v b/theories/Arith/EqNat.v index 82d05e2c..a9244455 100644 --- a/theories/Arith/EqNat.v +++ b/theories/Arith/EqNat.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: EqNat.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: EqNat.v 9966 2007-07-10 23:54:53Z letouzey $ i*) (** Equality on natural numbers *) @@ -89,3 +89,13 @@ Proof. intros n H1 H2. discriminate H2. intros n H1 z H2 H3. case (H2 _ H3). reflexivity. Defined. + +Lemma beq_nat_true : forall x y, beq_nat x y = true -> x=y. +Proof. + induction x; destruct y; simpl; auto; intros; discriminate. +Qed. + +Lemma beq_nat_false : forall x y, beq_nat x y = false -> x<>y. +Proof. + induction x; destruct y; simpl; auto; intros; discriminate. +Qed. |