proposition: Lemma invbinophrelandfun {X Y : setwithbinop} (f : binopfun X Y) (R : hrel Y) (is : @isinvbinophrel Y R) : @isinvbinophrel X (λ x x', R (f x) (f x')).
proof: Proof. set (ish := (pr2 f) : ∏ a0 b0, paths (f (op a0 b0)) (op (f a0) (f b0))). split. - intros a b c r. rewrite (ish _ _) in r. rewrite (ish _ _) in r. apply ((pr1 is) _ _ _ r). - intros a b c r. rewrite (ish _ _) in r. rewrite (ish _ _) in r. apply ((pr2 is) _ _ _ r). Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.Propositions