Definition is_nat_trans_RelMonadMor {C : precategory_data} {D: precategory} {J : functor C D} {R R' : RelMonad J} (α : RelMonadMor R R'): is_nat_trans (R_functor R) (R_functor R') (α:RelMonadMor_data R R'). Proof. red. intros c c' f. unfold R_functor; simpl. unfold r_lift; simpl. rewrite <- (α_r_bind α). rewrite <- assoc. now rewrite (r_eta_α α). 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.