Definition acommring_hzmod ( p : hz ) ( x : hzneq 0 p ) : acommring. Proof. intros. split with ( hzmodp p x ). split with ( tpair _ ( deceqtoneqapart ( isdeceqhzmodp p x ) ) ). split. - split. + intros a b c q. simpl. simpl in q. intro f. apply q. rewrite f. apply idpath. + intros a b c q. simpl in q. simpl. intro f. apply q. rewrite f. apply idpath. - split. + intros a b c q. simpl in q. simpl. intros f. apply q. rewrite f. apply idpath. + intros a b c q. simpl. simpl in q. intro f. apply q. rewrite f. apply idpath. Defined.
Require Import UniMath.PAdics.lemmas. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Foundations.Preamble.