Proposition lunitor_twosided_disp_nat_trans_hor_comp {C₁ C₂ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {F : C₁ ⟶ C₂} {FF : twosided_disp_functor F F D₁ D₂} {Cm₁ : hor_comp D₁} {Cm₂ : hor_comp D₂} (FI : double_functor_hor_comp FF Cm₁ Cm₂) : double_nat_trans_hor_comp (id_twosided_disp_nat_trans _) (comp_hor_comp (identity_hor_comp _) FI) FI. Proof. intros x y z h k ; cbn. rewrite double_hor_comp_mor_id. rewrite two_disp_pre_whisker_b. rewrite id_two_disp_right. rewrite transport_b_b_disp_mor2. rewrite id_two_disp_left. rewrite transport_b_b_disp_mor2. rewrite twosided_disp_functor_id. rewrite two_disp_post_whisker_b. rewrite transport_b_b_disp_mor2. rewrite id_two_disp_right. rewrite transport_b_b_disp_mor2. use transportf_disp_mor2_eq. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. 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.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor.