diff options
| -rw-r--r-- | theories/Arith/PeanoNat.v | 10 |
1 files changed, 2 insertions, 8 deletions
diff --git a/theories/Arith/PeanoNat.v b/theories/Arith/PeanoNat.v index ffa56a6c3..95fd4cf86 100644 --- a/theories/Arith/PeanoNat.v +++ b/theories/Arith/PeanoNat.v @@ -172,15 +172,9 @@ Proof. apply leb_le. Qed. - -Lemma leb_not_le n m : (n <=? m) = false -> n > m. +Lemma leb_not_le n m : (n <=? m) = false <-> ~n <= m. Proof. - revert m; induction n; destruct m; simpl; intros H_nm. - - congruence. - - congruence. - - apply lt_succ_r, le_0_n. - - specialize (IHn _ H_nm). - now apply lt_succ_r in IHn. + now rewrite <- leb_le, <- not_true_iff_false. Qed. (** ** Decidability of equality over [nat]. *) |