Lemma abgr_natnat_hz_X_comm {X : abgr} (x : X) : monoidfuncomp hz_abmonoid_monoidfun (hz_abgr_fun_monoidfun x) = nat_nat_prod_abmonoid_monoidfun x. Proof. use monoidfun_paths. use funextfun. intros n. use setquotunivcomm. Qed.
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.