Lemma abmonoidfracrellogeq (X : abmonoid) (A : subabmonoid X) {L L' : hrel X} (is : ispartbinophrel A L) (is' : ispartbinophrel A L') (lg : ∏ x x', L x x' <-> L' x x') (x x' : abmonoidfrac X A) : (abmonoidfracrel X A is x x') <-> (abmonoidfracrel X A is' x x'). Proof. apply quotrellogeq. intros x0 x0'. split. - unfold abmonoidfracrelint. simpl. apply hinhfun. intro t2. exists (pr1 t2). apply (pr1 (lg _ _) (pr2 t2)). - unfold abmonoidfracrelint. simpl. apply hinhfun. intro t2. exists (pr1 t2). apply (pr2 (lg _ _) (pr2 t2)). Qed.
Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.Monoids2.