Lemma commringaddinvunique ( X : commring ) ( a b c : X ) ( p : @op1 X a b = @ringunel1 X ) ( q : @op1 X a c = @ringunel1 X ) : b = c. Proof. intros. rewrite ( pathsinv0 ( ringrunax1 X b ) ). rewrite ( pathsinv0 q ). rewrite ( pathsinv0 ( ringassoc1 X _ _ _ ) ). rewrite ( ringcomm1 X b _ ). rewrite p. rewrite ringlunax1. 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.