Definition is_nat_trans_r_eta {C: precategory_data} {D: precategory} {J : functor C D}(R : RelMonad) : is_nat_trans J (R_functor R) (r_eta R). Proof. red. intros c c' f. unfold R_functor; simpl. unfold r_lift; simpl. apply pathsinv0. apply (r_eta_r_bind R). 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.