Lemma hzmodcompatplusr ( p : hz ) ( x : hzneq 0 p ) : forall a b c : hz, hzmod p x a b -> hzmod p x ( a + c ) ( b + c ). Proof. intros a b c v. rewrite hzpluscomm. rewrite ( hzpluscomm b ). apply hzmodcompatplusl. assumption. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.