Lemma hzremaindermoditerated ( m : hz ) ( is : hzneq 0 m ) ( n : hz ) : hzremaindermod m is ( hzremaindermod m is n ) = ( hzremaindermod m is n ). Proof. intros. apply pathsinv0. apply ( hzqrtestr 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.