proposition: Lemma compare_le_iff n m : (n ?= m) <> Gt <-> n <= m.
proof: Proof. revert m; induction n as [|n IHn]; intro m; destruct m; simpl; rewrite ?IHn. - now split. - split; intros. + apply Peano.le_0_n. + easy. - split. + now destruct 1. + inversion 1. - split; intros. + now apply Peano.le_n_S. + now apply Peano.le_S_n. Qed.
imports: NAxioms NProperties OrdersFacts DecidableClass