Lemma carryandremainder ( a : fpscommring hz ) ( n : nat ) : hzremaindermod m is ( carry a n ) = carry a n. Proof. intros. unfold carry. rewrite hzremaindermoditerated. 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.