Lemma nat_to_monoid_fun_unel {X : monoid} (x : X) : nat_to_monoid_fun x O = (unel X). Proof. exact (idpath (unel X)). Defined.
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.