Definition double_cat_horizontal_cells_are_squares (H : ver_weq_square C) : horizontally_saturated double_cat_to_verity_double_bicat. Proof. refine (λ (x y : C) (v₁ v₂ : x -->v y), _). use isweqimplimpl. - cbn. intros s. exact (invmap (make_weq _ (H x y v₁ v₂)) s). - apply homset_property. - apply isaprop_square_ver_weq_square. exact H. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.DiscreteBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.Core. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints. Require Import UniMath.Bicategories.DoubleCategories.Underlying.HorizontalBicategory.