Definition make_double_functor_hor_comp_double_cat {C₁ C₂ : univalent_double_cat} (F : C₁ ⟶ C₂) (FF : twosided_disp_functor F F (hor_mor C₁) (hor_mor C₂)) (FFc : ∏ (x y z : C₁) (h : x -->h y) (k : y -->h z), square (identity_v _) (identity_v _) (FF _ _ h ·h FF _ _ k) (FF _ _ (h ·h k))) (HFFc : ∏ (x₁ x₂ y₁ y₂ z₁ z₂ : C₁) (v₁ : x₁ -->v x₂) (v₂ : y₁ -->v y₂) (v₃ : z₁ -->v z₂) (h₁ : x₁ -->h y₁) (h₂ : x₂ -->h y₂) (k₁ : y₁ -->h z₁) (k₂ : y₂ -->h z₂) (s₁ : square v₁ v₂ h₁ h₂) (s₂ : square v₂ v₃ k₁ k₂), (#2 FF s₁ ⋆h #2 FF s₂) ⋆v FFc _ _ _ h₂ k₂ = transportb_square (id_v_right _ @ !(id_v_left _)) (id_v_right _ @ !(id_v_left _)) (FFc _ _ _ h₁ k₁ ⋆v #2 FF (s₁ ⋆h s₂))) : double_functor_hor_comp FF (hor_comp_double_cat C₁) (hor_comp_double_cat C₂) := FFc ,, HFFc.
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.