Lemma isinjnatcoface ( i x y : nat ) : natcoface i x = natcoface i y -> x = y. Proof. intros p. change x with ( idfun _ x). rewrite <- ( natcofaceretractisretract i ). change y with ( idfun _ y ). rewrite <- ( natcofaceretractisretract i ). simpl. rewrite p. apply idpath. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Algebra.Monoids.