Proposition identity_functor_lunitor {C : category} {D : twosided_disp_cat C C} {I : hor_id D} {Cm : hor_comp D} (l : double_cat_lunitor I Cm) : double_functor_lunitor l l (identity_hor_id I) (identity_hor_comp Cm). Proof. intros x y f ; cbn. rewrite double_hor_comp_mor_id. rewrite id_two_disp_left. unfold transportb_disp_mor2. rewrite two_disp_pre_whisker_f. rewrite transport_f_f_disp_mor2. rewrite id_two_disp_left. unfold transportb_disp_mor2. rewrite transport_f_f_disp_mor2. refine (!_). apply transportf_disp_mor2_idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.