Proposition square_id_left_v' {C : double_cat} {x₁ x₂ y₁ y₂ : C} {v₁ : x₁ -->v y₁} {v₂ : x₂ -->v y₂} {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} (s : square v₁ v₂ h₁ h₂) : transportf_square (id_left _) (id_left _) (id_v_square h₁ ⋆v s) = s. Proof. rewrite square_id_left_v. rewrite transportfb_square. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats.