proposition: Lemma mult_a_1 : forall a, nf a -> a * 1 = a.
proof: Proof. induction a. - reflexivity. - cbn; simpl in IHa2. intro H; case_eq a1. intro; subst a1; rewrite Nat.mul_1_r. now rewrite (nf_of_finite H). intros; subst a1; now rewrite Nat.mul_1_r. Qed.
imports: Coq(Arith Max Bool Lia Compare_dec Relations Ensembles Wellfounded Bool RelationClasses Operators_Properties ArithRing Logic.Eqdep_dec) hydras(More_Arith Restriction DecPreOrder) hydras(OrdNotations)