Lemma hzqrand1ineq ( p : hz ) ( is : isaprime p ) : hzleh 0 1 × hzlth 1 ( nattohz ( hzabsval p ) ). Proof. intros. split. - apply hzlthtoleh. apply hzlthnsn. - rewrite hzabsvalgth0. + apply is. + apply ( istranshzgth _ 1 _ ). * apply is. * apply ( hzgthsnn 0 ). Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.