Lemma carryandtimes ( a b : fpscommring hz ) : carry ( a * b ) = carry ( carry a * carry b ). Proof. intros. rewrite carryandtimesl. rewrite carryandtimesr. 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.