Definition neqchoicelogeqf {X : UU} {L R : hrel X} (lg : ∏ x1 x2, L x1 x2 <-> R x1 x2) (isl : neqchoice L) : neqchoice R. Proof. intros. intros x1 x2 ne. apply (coprodf (pr1 (lg x1 x2)) (pr1 (lg x2 x1)) (isl _ _ ne)). Defined.
Require Import UniMath.Foundations.UnivalenceAxiom.