proposition: Lemma smf_from_param_distr_bicat_is_strong2_inv_ok (vw : Mon_V ⊠ Mon_V): is_inverse_in_precat (lax_monoidal_functor_μ lmf_from_param_distr_bicat vw) (smf_from_param_distr_bicat_is_strong2_inv vw).
proof: Proof. split. - use total2_paths_f. + cbn. apply id_right. + apply trafotargetbicat_disp_cells_isaprop. - use total2_paths_f. + cbn. apply id_right. + apply trafotargetbicat_disp_cells_isaprop. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.DisplayedMonoidalTensored UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ActionBasedStrength UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Examples.BicatOfCats