Lemma hzmodissymm ( p : hz ) ( x : hzneq 0 p ) : issymm ( hzmod p x ). Proof. intros. unfold issymm. intros n m. unfold hzmod. intro v. assert ( hzremaindermod p x m = hzremaindermod p x n ) as a by exact ( pathsinv0 v ). apply a. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.