Lemma nattorig_mult : ∏ {X : rig} (n m : nat), (nattorig (n * m) : X) = (nattorig n * nattorig m)%rig. Proof. intros X n m. unfold nattorig. rewrite (natmult_mult (X := rigaddabmonoid X)), <- nattorig_natmult. reflexivity. Qed.
Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.DivisionRig. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.ConstructiveStructures. Require Import UniMath.MoreFoundations.Tactics.