Definition hor_comp_hor_opposite_double_cat_data : hor_comp_data (hor_op_twosided_disp_cat (hor_mor C)). Proof. use make_hor_comp_data. - exact (λ (x y z : C) (h : y -->h x) (k : z -->h y), k ·h h). - exact (λ (x₁ x₂ y₁ y₂ z₁ z₂ : C) (v₁ : x₁ -->v x₂) (v₂ : y₁ -->v y₂) (v₃ : z₁ -->v z₂) (h₁ : y₁ -->h x₁) (h₂ : z₁ -->h y₁) (k₁ : y₂ -->h x₂) (k₂ : z₂ -->h y₂) (s₁ : square v₂ v₁ h₁ k₁) (s₂ : square v₃ v₂ h₂ k₂), s₂ ⋆h s₁). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Opposites. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.PseudoDoubleSetCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.Variations. Require Import UniMath.Bicategories.DoubleCategories.Underlying.HorizontalBicategory.