Definition double_coalg_sqr {X₁ X₂ Y₁ Y₂ : double_coalg F} (v : double_coalg_ver X₁ X₂) (w : double_coalg_ver Y₁ Y₂) (h₁ : double_coalg_hor X₁ Y₁) (h₂ : double_coalg_hor X₂ Y₂) : UU := h₁ -->[ v ][ w ] h₂. Coercion sqr_of_double_coalg_sqr {X₁ X₂ Y₁ Y₂ : double_coalg F} {v : double_coalg_ver X₁ X₂} {w : double_coalg_ver Y₁ Y₂} {h₁ : double_coalg_hor X₁ Y₁} {h₂ : double_coalg_hor X₂ Y₂} (s : double_coalg_sqr v w h₁ h₂) : square v w h₁ h₂. Proof. exact (pr1 s). Defined.
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.FunctorCoalgebras. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. 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.Total. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.DispCatOnTwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.TwoSidedDispCatOnDispCat. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws. Import TransportSquare.