Lemma iscomptoabmonoidfrac (X : abmonoid) (A : submonoid X) {L : hrel X} (is : ispartbinophrel A L) : iscomprelrelfun L (abmonoidfracrel X A is) (toabmonoidfrac X A). Proof. unfold iscomprelrelfun. intros x x' l. change (abmonoidfracrelint X A L (x ,, unel A) (x' ,, unel A)). simpl. apply (hinhpr). exists (unel A). apply ((pr2 is) _ _ 0). apply (pr2 (unel A)). apply ((pr2 is) _ _ 0). apply (pr2 (unel A)). apply l. Qed.
Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.Monoids2.