Definition isantisymmneglogeqf {X : UU} {L R : hrel X} (lg : ∏ x1 x2, L x1 x2 <-> R x1 x2) (isl : isantisymmneg L) : isantisymmneg R. Proof. intros. intros x1 x2 nr12 nr21. apply (isl _ _ (negf (pr1 (lg _ _)) nr12) (negf (pr1 (lg _ _)) nr21)). Defined.
Require Import UniMath.Foundations.UnivalenceAxiom.