Definition disp_actionbicat_disp_comp_nat_trans_data {a0 a1 a2 : B} {g1 : B ⟦ a0, a1 ⟧} {g2 : B ⟦ a1, a2 ⟧} {FA : V ⟶ category_from_bicat_and_ob a0} {FAm : fmonoidal Mon_V (monoidal_from_bicat_and_ob a0) FA} {FA' : V ⟶ category_from_bicat_and_ob a1} {FA'm : fmonoidal Mon_V (monoidal_from_bicat_and_ob a1) FA'} {FA'' : V ⟶ category_from_bicat_and_ob a2} {FA''m : fmonoidal Mon_V (monoidal_from_bicat_and_ob a2) FA''} (Hyp1 : disp_actionbicat_disp_mor FAm FA'm g1) (Hyp2 : disp_actionbicat_disp_mor FA'm FA''m g2): nat_trans_data (H(V:=V)(FA':=FA'') (g1 · g2)) (H'(FA:=FA) (g1 · g2)). Proof. intro v. cbn. exact (rassociator g1 g2 (FA'' v) • ((g1 ◃ (pr1 Hyp2 v)) • ((lassociator g1 (FA' v) g2 • ((pr1 Hyp1 v) ▹ g2) : g1 · H' g2 v ==> FA v · g1 · g2) • rassociator (FA v) g1 g2))). 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrongFunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.Core.Invertible_2cells. Import Bicat.Notations. Import BifunctorNotations. Import DisplayedBifunctorNotations.