Definition prabmonoidfrac (X : abmonoid) (A : submonoid X) : X → A → abmonoidfrac X A := λ (x : X) (a : A), setquotpr (eqrelabmonoidfrac X A) (x ,, a).
Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.Monoids2.