Lemma isbinopabgrdiffrelint (X : abmonoid) {L : hrel X} (is : isbinophrel L) : @isbinophrel (setwithbinopdirprod X X) (abgrdiffrelint X L). Proof. apply (isbinophrellogeqf (logeqabgrdiffrelints X L)). split. - intros a b c lab. apply (pr1 (ispartbinopabmonoidfracrelint _ (totalsubmonoid X) (isbinoptoispartbinop _ _ is)) (abgrdiffphi X a) (abgrdiffphi X b) (abgrdiffphi X c) tt lab). - intros a b c lab. apply (pr2 (ispartbinopabmonoidfracrelint _ (totalsubmonoid X) (isbinoptoispartbinop _ _ is)) (abgrdiffphi X a) (abgrdiffphi X b) (abgrdiffphi X c) tt lab). Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Subtypes.