proposition: Lemma lt_mul_mono' : forall c a b, a < b -> a < b * (S c).
proof: Proof. induction c; intros. rewrite Nat.mul_1_r; auto. rewrite Nat.mul_succ_r. apply Nat.lt_lt_add_r. apply IHc; 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