Definition make_double_functor_associator_double_cat {C₁ C₂ : univalent_double_cat} (F : C₁ ⟶ C₂) (FF : twosided_disp_functor F F (hor_mor C₁) (hor_mor C₂)) (FC : double_functor_hor_comp FF (hor_comp_double_cat C₁) (hor_comp_double_cat C₂)) (H : ∏ (w x y z : C₁) (h₁ : w -->h x) (h₂ : x -->h y) (h₃ : y -->h z), lassociator_h (FF _ _ h₁) (FF _ _ h₂) (FF _ _ h₃) ⋆v (functor_double_comp_cell FC h₁ h₂ ⋆h id_v_square _) ⋆v functor_double_comp_cell FC (h₁ ·h h₂) h₃ = transportf_square (maponpaths _ (functor_id _ _)) (maponpaths _ (functor_id _ _)) ((id_v_square _ ⋆h functor_double_comp_cell FC h₂ h₃) ⋆v functor_double_comp_cell FC h₁ (h₂ ·h h₃) ⋆v #2 FF (lassociator_h h₁ h₂ h₃))) : double_functor_associator (double_cat_double_associator C₁) (double_cat_double_associator C₂) FC.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfDispCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfTwoSidedDispCat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleTransformation. Require Import UniMath.Bicategories.DoubleCategories.Core.BicatOfDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats.