Lemma hzqrand1q ( p : hz ) ( is : isaprime p ) : hzquotientmod p ( isaprimetoneq0 is ) 1 = 0. Proof. intros. apply pathsinv0. apply ( hzqrtestq p ( isaprimetoneq0 is ) 1 0 1 ). split. - apply ( hzqrand1eq p is ). - apply ( hzqrand1ineq p is ). Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.