Definition hzlthremaindermodmod ( p : hz ) ( x : hzneq 0 p ) ( n : hz ) : hzlth ( hzremaindermod p x n ) ( nattohz ( hzabsval p ) ) := pr2 ( pr2 ( pr2 ( divalgorithmexists n p x ) ) ).
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.