Proposition rinvunitor_twosided_disp_nat_trans_hor_id {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} {I₁ : hor_id D₁} {I₂ : hor_id D₂} (FI : double_functor_hor_id FF I₁ I₂) : double_nat_trans_hor_id (id_twosided_disp_nat_trans _) FI (comp_hor_id FI (identity_hor_id _)). Proof. intros x ; cbn. rewrite double_id_mor_id. rewrite id_two_disp_left. unfold transportb_disp_mor2. rewrite transport_f_f_disp_mor2. rewrite id_two_disp_right. unfold transportb_disp_mor2. rewrite transport_f_f_disp_mor2. rewrite id_two_disp_left. unfold transportb_disp_mor2. rewrite transport_f_f_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.