proposition: Proposition full_local_equivalence_mnd_eq : local_equivalence_mnd_data_mor full_local_equivalence_mnd_cell = τ.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax UniMath.Bicategories.Monads.Examples.PsfunctorOnMonad UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties UniMath.Bicategories.PseudoFunctors.LocalEquivalenceProperties UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion