Proposition double_cat_to_is_predoublecategory_hor_sq : is_predoublecategory_hor_sq double_cat_to_predoublecategory_sq_hor_data. Proof. repeat split. - intro ; intros ; cbn. apply (square_id_left_v (C := C)). - intro ; intros ; cbn. apply (square_id_right_v (C := C)). - intro ; intros ; cbn. apply (square_assoc_v (C := C)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. 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.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.BicatOfDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.AlternativeDefinitions.DoubleCatsUnfolded.