proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics