Lemma hzqrandtimesineq ( m : hz ) ( x : hzneq 0 m ) ( a b : hz ) : hzleh 0 ( hzremaindermod m x ( hzremaindermod m x a * hzremaindermod m x b ) ) × hzlth ( hzremaindermod m x ( hzremaindermod m x a * hzremaindermod m x b ) ) ( nattohz ( hzabsval m ) ). Proof. intros. split. - apply hzleh0remaindermod. - apply hzlthremaindermodmod. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.