Lemma hzmodistrans ( p : hz ) ( x : hzneq 0 p ) : istrans ( hzmod p x ). Proof. intros. unfold istrans. intros n m k. intros u v. unfold hzmod. unfold hzmod in u. unfold hzmod in v. assert ( hzremaindermod p x n = hzremaindermod p x k ) as a by exact ( pathscomp0 u v ). apply a. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.