proposition: Lemma smf_from_param_distr_bicat_is_strong2_aux (vw : Mon_V ⊠ Mon_V): pr2 (monoidal_functor_map_codom Mon_V montrafotargetbicat_moncat lmf_from_param_distr_bicat vw) -->[id pr1 (monoidal_functor_map_codom Mon_V montrafotargetbicat_moncat lmf_from_param_distr_bicat vw)] pr2 (monoidal_functor_map_dom Mon_V montrafotargetbicat_moncat lmf_from_param_distr_bicat vw).
proof: Proof. unfold mor_disp. unfold trafotargetbicat_disp. hnf. red in δpe_eq. do 2 rewrite functor_id. rewrite id_left, id_right. cbn. assert (δpe_eqinst := δpe_eq (pr1 vw) (pr2 vw)). exact δpe_eqinst. 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