Lemma mlift_id {R : RelMonad_data J} {M : RelModule_data R} (X : RelModule_laws M) (c : C) : mlift M (identity c) = identity (M c). Proof. transitivity (mbind M (r_eta R c)). 2: apply (mbind_r_eta X). unfold mlift. cbn. apply maponpaths. etrans. 2: apply id_left. apply maponpaths_2. apply functor_id. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monads.RelativeMonads.