Lemma hzmodcompatplusl ( p : hz ) ( x : hzneq 0 p ) : forall a b c : hz, hzmod p x a b -> hzmod p x ( c + a ) ( c + b ). Proof. intros a b c v. unfold hzmod. change ( hzremaindermod p x ( c + a ) = hzremaindermod p x ( c + b ) ). rewrite hzremaindermodandplus. rewrite v. rewrite <- hzremaindermodandplus. apply idpath. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.