Definition bicat_to_hor_comp_data : hor_comp_data bicat_to_twosided_disp_cat. Proof. use make_hor_comp_data. - exact (λ x y z f g, f · g). - intros x₁ x₂ y₁ y₂ z₁ z₂ p₁ p₂ p₃ f₁ f₂ g₁ g₂ s₁ s₂. induction p₁, p₂, p₃ ; cbn in *. exact (rassociator _ _ _ • (_ ◃ s₂) • lassociator _ _ _ • (s₁ ▹ _) • rassociator _ _ _). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Strictness. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.PseudoDoubleSetCats.