Definition parameterized_distributivity_nat_as_instance (δtr: parameterized_distributivity_nat Mon_V A A' FA FA' G): parameterized_distributivity_bicat_nat FA FA' G. Proof. red. red in δtr. unfold Main.H, Main.H'. unfold param_distributivity_dom, param_distributivity_codom in δtr. use make_nat_trans. - exact (pr1 δtr). - intros v w f. cbn. set (δtr_nat_inst := pr2 δtr v w f). cbn in δtr_nat_inst. unfold pre_whisker_in_funcat, post_whisker_in_funcat in δtr_nat_inst. rewrite post_whisker_identity. rewrite pre_whisker_identity. rewrite (nat_trans_comp_id_left A' (functor_composite G ((pr11 FA') v)) (functor_composite G ((pr11 FA') w))). rewrite (nat_trans_comp_id_right A' (functor_composite ((pr11 FA) v) G) (functor_composite ((pr11 FA) w) G)). exact δtr_nat_inst. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.DisplayedMonoidalTensored. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.Actions. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrength. Require Import UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Import Bicat.Notations.