Lemma iscoasymmabmonoidfracrelint (X : abmonoid) (A : subabmonoid X) {L : hrel X} (is : ispartbinophrel A L) (isl : iscoasymm L) : iscoasymm (abmonoidfracrelint X A L). Proof. intros. set (assoc := (assocax X) : isassoc (@op X)). unfold isassoc in assoc. set (comm := commax X). unfold iscomm in comm. unfold iscoasymm. intros xa1 xa2. intro nl0. set (nl := neghexisttoforallneg _ nl0 (unel A)). simpl in nl. set (l := isl _ _ nl). apply hinhpr. exists (unel A). apply l. Qed.
Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.Monoids2.