Definition is_flat_double_cat (C : double_cat) : UU := ∏ (x₁ x₂ y₁ y₂ : C) (v₁ : x₁ -->v y₁) (v₂ : x₂ -->v y₂) (h₁ : x₁ -->h x₂) (h₂ : y₁ -->h y₂) (s₁ s₂ : square v₁ v₂ h₁ h₂), s₁ = 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.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.