Lemma minussn1non0 ( n : nat ) ( p : natlth 0 n ) : S ( sub n 1 ) = n. Proof. revert p. destruct n. - intro p. apply fromempty. exact (isirreflnatlth 0%nat p ). - intro. apply maponpaths. apply minus0r. 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.