Definition is_double_coalg_sqr {C : univalent_double_cat} {F : lax_double_functor C C} {X₁ : double_coalg F} {Y₁ : double_coalg F} {f₁ : X₁ -->h Y₁} (s₁ : square (double_coalg_map X₁) (double_coalg_map Y₁) f₁ (#h F f₁)) {X₂ : double_coalg F} {Y₂ : double_coalg F} {f₂ : X₂ -->h Y₂} (s₂ : square (double_coalg_map X₂) (double_coalg_map Y₂) f₂ (#h F f₂)) (v : double_coalg_ver X₁ X₂) (w : double_coalg_ver Y₁ Y₂) (r : square v w f₁ f₂) : UU := transportf_square (double_coalg_ver_comm v) (double_coalg_ver_comm w) (s₁ ⋆v #s F r) = r ⋆v s₂.
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.