proposition: Lemma mult_lt_compat : forall a b c d, a < b -> c < d -> a * c < b * d.
proof: Proof. intuition. eapply Nat.le_lt_trans. eapply Nat.mul_le_mono. assert (a <= b). lia. eapply H1. eapply Nat.le_refl. apply Nat.mul_lt_mono_pos_l; lia. Qed.
imports: Arith micromega.Lia Coq.NArith.BinNat