Definition make_double_functor_hor_id_double_cat {C₁ C₂ : univalent_double_cat} (F : C₁ ⟶ C₂) (FF : twosided_disp_functor F F (hor_mor C₁) (hor_mor C₂)) (FFi : ∏ (x : C₁), square (identity_v (F x)) (identity_v (F x)) (identity_h (F x)) (FF x x (identity_h x))) (HFFi : ∏ (x y : C₁) (v : x -->v y), id_h_square (#F v) ⋆v FFi y = transportb_square (id_v_right _ @ !(id_v_left _)) (id_v_right _ @ !(id_v_left _)) (FFi x ⋆v #2 FF (id_h_square v))) : double_functor_hor_id FF (hor_id_double_cat C₁) (hor_id_double_cat C₂) := FFi ,, HFFi.
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.