proposition: Lemma hzqrand0q ( p : hz ) ( x : hzneq 0 p ) : hzquotientmod p x 0 = 0.
proof: Proof. intros. apply pathsinv0. apply ( hzqrtestq p x 0 0 0 ). split. - apply ( hzqrand0eq p x ). - apply ( hzqrand0ineq p x ). Defined.
imports: UniMath.PAdics.lemmas UniMath.NumberSystems.Integers UniMath.Foundations.Preamble