proposition: Lemma compare_lt_iff n m : (n ?= m) = Lt <-> n < m.
proof: Proof. revert m; induction n as [|n IHn]; intro m; destruct m; simpl; rewrite ?IHn; split; try easy. - intros _; apply Peano.le_n_S, Peano.le_0_n. - apply Peano.le_n_S. - apply Peano.le_S_n. Qed.
imports: NAxioms NProperties OrdersFacts DecidableClass