Lemma hzmodcompatmultl ( 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 hzremaindermodandtimes. rewrite v. rewrite <- hzremaindermodandtimes. apply idpath. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.