proposition: Proposition local_equivalence_mnd_data_mor_laws : is_mnd_cell local_equivalence_mnd_data_mor_data.
proof: Proof. unfold is_mnd_cell ; cbn ; unfold local_equivalence_mnd_data_mor_data. rewrite !vassocl. etrans. { do 3 apply maponpaths. rewrite lwhisker_hcomp. rewrite <- linvunitor_natural. apply idpath. } rewrite !vassocr. apply maponpaths_2. rewrite vcomp_whisker. rewrite !vassocl. apply maponpaths. rewrite <- local_equivalence_inv_twocell_comp. rewrite !vassocl. rewrite <- vcomp_lunitor. etrans. { apply maponpaths. rewrite !vassocr. etrans. { apply maponpaths. apply maponpaths_2. exact (mnd_cell_endo τ). } rewrite !vassocl. apply local_equivalence_inv_twocell_comp. } rewrite !vassocr. apply maponpaths_2. use vcomp_move_R_pM ; [ is_iso | ]. rewrite !vassocr. use vcomp_move_L_Mp ; [ is_iso | ]. cbn. rewrite local_equivalence_twocell_rwhisker. apply idpath. 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