Proposition lunitor_id_id_h {C : double_cat} (x : C) : lunitor_h (identity_h x ·h identity_h x) = id_h_square (identity_v x) ⋆h lunitor_h (identity_h x). Proof. refine (!(square_id_right_v' _) @ _ @ square_id_right_v' _). apply maponpaths. rewrite <- !lunitor_linvunitor_h'. rewrite !transportf_square_postwhisker. apply maponpaths. refine (square_assoc_v _ _ _ @ _ @ !(square_assoc_v _ _ _)). apply maponpaths. apply maponpaths_2. etrans. { rewrite <- lunitor_square'. apply idpath. } rewrite transportf_square_id. 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.DerivedLaws.Variations. Import TransportSquare.