Lemma hzmodisringeqrel ( p : hz ) ( x : hzneq 0 p ) : ringeqrel ( X := hz ). Proof. intros. split with ( tpair ( hzmod p x ) ( hzmodiseqrel p x ) ). split. - split. + apply hzmodcompatplusl. + apply hzmodcompatplusr. - split. + apply hzmodcompatmultl. + apply hzmodcompatmultr. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.