proposition: Lemma nattorig_natmult : ∏ {X : rig} (n : nat) (x : X), (nattorig n * x)%rig = natmult (X := rigaddabmonoid X) n x.
proof: Proof. intros. induction n as [|n IHn]. - now apply rigmult0x. - rewrite nattorigS, natmultS. now rewrite rigrdistr, IHn, riglunax2. Qed.
imports: UniMath.Foundations.NaturalNumbers UniMath.Algebra.RigsAndRings UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.Domains_and_Fields UniMath.Algebra.ConstructiveStructures UniMath.MoreFoundations.Tactics