proposition: Lemma o_finite_mult_mono : forall a b n, nf a -> nf b -> T1.lt a b -> T1.lt (o_finite_mult (S n) a) (o_finite_mult (S n) b).
proof: Proof. Proof with auto with T1. induction n. - simpl; repeat rewrite oplus_0_r;auto. - simpl; intros; apply oplus_strict_mono_bi ... apply oplus_nf;auto. apply o_finite_mult_nf;auto. apply oplus_nf;auto. apply o_finite_mult_nf;auto. Qed.
imports: Coq(Arith ArithRing Lia) hydras(Prelude.More_Arith Prelude.Merge_Sort Epsilon0.T1)