Lemma abgrdiffrellogeq (X : abmonoid) {L L' : hrel X} (is : isbinophrel L) (is' : isbinophrel L') (lg : ∏ x x', L x x' <-> L' x x') (x x' : abgrdiff X) : (abgrdiffrel X is x x') <-> (abgrdiffrel X is' x x'). Proof. refine (quotrellogeq _ _ _ _ _). intros x0 x0'. split. - simpl. apply hinhfun. intro t2. exists (pr1 t2). apply (pr1 (lg _ _) (pr2 t2)). - simpl. apply hinhfun. intro t2. exists (pr1 t2). apply (pr2 (lg _ _) (pr2 t2)). Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Subtypes.