proposition: Lemma lt_mul_mono : forall a b c, c <> 0 -> a < b -> a < b * c.
proof: Proof. intros. replace c with (S (c - 1)) by lia. apply lt_mul_mono'; auto. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Bool.Bool Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith bbv.N_Z_nat_conversions bbv.Nomega