proposition: Lemma mult_1_a : forall a, nf a -> 1 * a = a.
proof: Proof. induction a. - reflexivity. - cbn; simpl in IHa2. intro H; case_eq a1. + intro; subst a1; rewrite (nf_of_finite H); now rewrite <- (plus_n_O n). + intros t n0 t0 H0; subst a1; rewrite IHa2. * reflexivity. * eapply nf_inv2;eauto. 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)