proposition: 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: 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.
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