proposition: Lemma nat_nat_to_monoid2 {X : gr} (x : X) {n1 m1 n2 : nat} (e : n1 = m1) : nat_nat_to_monoid_fun x (make_dirprod n1 n2) = nat_nat_to_monoid_fun x (make_dirprod m1 n2).
proof: Proof. induction e. use idpath. Qed.
imports: UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.PartA UniMath.MoreFoundations.NegativePropositions UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.Algebra.RigsAndRings UniMath.NumberSystems.NaturalNumbersAlgebra