proposition: Theorem mul_eq_0_l : ∀ n m, n * m = 0 → m ≠ 0 → n = 0.
proof: Proof. intros n m Hnm Hm. destruct n as [n| ]; [ idtac | assumption ]. destruct m as [m| ]; simpl in Hnm; [ idtac | contradiction ]. injection Hnm; clear Hnm; intros Hnm. apply Nat.mul_eq_0_l in Hnm; [ subst n; reflexivity | idtac ]. intros H; apply Hm; subst m; reflexivity. Qed.
imports: Utf8 Compare_dec NPeano Misc