Lemma hzqrandremaindereq ( m : hz ) ( is : hzneq 0 m ) ( n : hz ) : hzremaindermod m is n = ( ( m * ( pr1 ( make_dirprod 0 ( hzremaindermod m is n ) ) ) + ( pr2 ( make_dirprod (@ringunel1 hz ) ( hzremaindermod m is n ) ) ) ) ). Proof. intros. simpl. rewrite hzmultx0. rewrite hzplusl0. apply idpath. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.