Lemma natcofaceleh ( i n upper : nat ) ( p : natleh n upper ) : natleh ( natcoface i n ) ( S upper ). Proof. intros. unfold natcoface. destruct ( natgtb i n ). - apply natlthtoleh. apply (natlehlthtrans _ upper ). + assumption. + apply natlthnsn. - apply p. 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.