Definition isirrefllogeqf {X : UU} {L R : hrel X} (lg : ∏ x1 x2, L x1 x2 <-> R x1 x2) (isl : isirrefl L) : isirrefl R. Proof. intros. intros x r. apply (isl _ (pr2 (lg x x) r)). Defined.
Require Import UniMath.Foundations.UnivalenceAxiom.