Lemma relmonad_eq_from_relmonad_z_iso_idtoiso {C : precategory_data} {D : category} (H: is_univalent D) (J : functor C D) {R R': RelMonad J} (p: R = R') : relmonad_eq_from_relmonad_z_iso H J (idtoiso(C := category_RelMonad D J) p) = p. Proof. apply relmonad_eq_eq_from_relmonad_ob_eq. - apply D. - unfold relmonad_eq_from_relmonad_z_iso. unfold RelMonad_eq. rewrite base_total2_paths. rewrite base_total2_paths. apply pr1_pr1_relmonadmor_eq_from_relmonadmor_z_iso_idtoiso. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core.