Lemma mlift_mbind {c d e : C} (f : c --> d) (g : J d --> R e) : mlift M f · mbind M g = mbind M (#J f · g). Proof. unfold mlift. etrans. { apply (mbind_mbind X). } apply maponpaths. etrans. { apply pathsinv0, assoc. } apply maponpaths. apply (r_eta_r_bind R). 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.