Proposition full_local_equivalence_mnd_eq : local_equivalence_mnd_data_mor full_local_equivalence_mnd_cell = τ. Proof. use eq_mnd_cell ; cbn. rewrite !vassocl. rewrite !local_equivalence_inv_twocell_comp. rewrite local_equivalence_counit_triangle. rewrite <- local_equivalence_unit_natural_alt. rewrite !vassocr. refine (_ @ id2_left _). apply maponpaths_2. etrans. { apply maponpaths_2. exact (local_equivalence_counit_triangle_inv HF (mor_of_mnd_mor f)). } apply vcomp_rinv. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Monads.Examples.PsfunctorOnMonad. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Properties. Require Import UniMath.Bicategories.PseudoFunctors.LocalEquivalenceProperties. Require Import UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion.