Lemma hzqrandcarryeq ( a : fpscommring hz ) ( n : nat ) : carry a n = m * 0 + carry a n. Proof. intros. rewrite hzmultx0. rewrite hzplusl0. apply idpath. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.PAdics.fps. Require Import UniMath.PAdics.frac. Require Import UniMath.PAdics.z_mod_p. Require Import UniMath.NumberSystems.Integers.