Lemma hzqrandremainderq ( m : hz ) ( is : hzneq 0 m ) ( n : hz ) : 0 = hzquotientmod m is ( hzremaindermod m is n ). Proof. intros. apply ( hzqrtestq m is ( hzremaindermod m is n ) 0 ( hzremaindermod m is n ) ). split. - apply hzqrandremaindereq. - apply hzqrandremainderineq. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.