diff options
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/Arith/PeanoNat.v | 11 |
1 files changed, 11 insertions, 0 deletions
diff --git a/theories/Arith/PeanoNat.v b/theories/Arith/PeanoNat.v index bde6f1bb4..ffa56a6c3 100644 --- a/theories/Arith/PeanoNat.v +++ b/theories/Arith/PeanoNat.v @@ -172,6 +172,17 @@ Proof. apply leb_le. Qed. + +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. +Qed. + (** ** Decidability of equality over [nat]. *) Lemma eq_dec : forall n m : nat, {n = m} + {n <> m}. |