Definition relmonad_eq_from_relmonad_z_iso_obsolete {C : precategory_data} {D : category} (H: is_univalent D) (J : functor C D) {R R': RelMonad J} (α : z_iso(C := category_RelMonad D J) R R') : R = R'. Proof. set (Hob := pr1_pr1_relmonadmor_eq_from_relmonadmor_z_iso H J α). assert (η_eq := η_relmonadmor_eq_from_relmonadmor_z_iso H J α). assert (bind_eq := bind_relmonadmor_eq_from_relmonadmor_z_iso H J α). fold Hob in η_eq, bind_eq. induction R as [[F [e b]] a]. induction R' as [[F' [e' b']] a']. simpl in Hob. induction Hob. cbn in η_eq, bind_eq. apply RelMonad_eq. + exact D. + simpl. apply maponpaths. apply pathsdirprod; assumption. Defined.
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.