proposition: Lemma isantisymmnegabgrdiffrel (X : abmonoid) {L : hrel X} (is : isbinophrel L) (isl : isantisymmneg L) : isantisymmneg (abgrdiffrel X is).
proof: Proof. apply (isantisymmneglogeqf (logeqabgrdiffrels X is)). intros a b rab rba. set (int := isantisymmnegabmonoidfracrel _ (totalsubmonoid X) (isbinoptoispartbinop _ _ is) isl (weqabgrdiff X a) (weqabgrdiff X b) rab rba). apply (invmaponpathsweq _ _ _ int). Defined.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Subtypes UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids