Lemma abmonoidfracrelimpl (X : abmonoid) (A : subabmonoid X) {L L' : hrel X} (is : ispartbinophrel A L) (is' : ispartbinophrel A L') (impl : ∏ x x', L x x' → L' x x') (x x' : abmonoidfrac X A) (ql : abmonoidfracrel X A is x x') : abmonoidfracrel X A is' x x'. Proof. generalize ql. apply quotrelimpl. intros x0 x0'. unfold abmonoidfracrelint. simpl. apply hinhfun. intro t2. exists (pr1 t2). apply (impl _ _ (pr2 t2)). Qed.
Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.Monoids2.