Lemma hzqrandremainderineq ( m : hz ) ( is : hzneq 0 m ) ( n : hz ) : hzleh ( @ringunel1 hz ) ( hzremaindermod m is n ) × hzlth ( hzremaindermod m is n ) ( 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.