Proposition identity_functor_associator {C : category} {D : twosided_disp_cat C C} {Cm : hor_comp D} (a : double_cat_associator Cm) : double_functor_associator a a (identity_hor_comp Cm). Proof. intros w x y z f g h ; cbn. rewrite id_two_disp_right. rewrite double_hor_comp_mor_id. rewrite id_two_disp_right. rewrite transport_b_b_disp_mor2. rewrite id_two_disp_right. rewrite double_hor_comp_mor_id. rewrite two_disp_pre_whisker_b. rewrite id_two_disp_left. rewrite transport_b_b_disp_mor2. use transportf_disp_mor2_eq. apply 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.