Lemma isapartdectodeceq { X : hSet } ( R : apart X ) ( is : isapartdec R ) : isdeceq X. Proof. intros y z. destruct ( is y z ) as [ l | r ]. - apply ii2. intros f. apply ( pr1 ( pr2 R ) z). rewrite f in l. assumption. - apply ii1. assumption. 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.