proposition: Lemma iscomptoabmonoidfrac (X : abmonoid) (A : submonoid X) {L : hrel X} (is : ispartbinophrel A L) : iscomprelrelfun L (abmonoidfracrel X A is) (toabmonoidfrac X A).
proof: Proof. unfold iscomprelrelfun. intros x x' l. change (abmonoidfracrelint X A L (make_dirprod x (unel A)) (make_dirprod x' (unel A))). simpl. apply (hinhpr). split with (unel A). apply ((pr2 is) _ _ 0). apply (pr2 (unel A)). apply ((pr2 is) _ _ 0). apply (pr2 (unel A)). apply l. Defined.
imports: UniMath.Algebra.BinaryOperations UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders