Lemma hzremaindermodandplus ( p : hz ) ( x : hzneq 0 p ) ( a c : hz ) : hzremaindermod p x ( a + c ) = hzremaindermod p x ( hzremaindermod p x a + hzremaindermod p x c ). Proof. intros. apply pathsinv0. apply ( hzqrtest p x ( a + c ) _ _ ( make_dirprod ( hzqrandpluseq p x a c ) ( hzqrandplusineq p x a c ) ) ). Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.