Lemma setquotprandpadicplus ( a b : fpscommring hz ) : @op1 commringofpadicints ( setquotpr ( carryequiv p ( isaprimetoneq0 is ) ) a ) ( setquotpr ( carryequiv p ( isaprimetoneq0 is ) ) b ) = setquotpr ( carryequiv p ( isaprimetoneq0 is ) ) ( a + b ). Proof. intros. apply commringquotprandop1. 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.