proposition: Proposition runitor_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} (FC : double_functor_hor_comp FF Cm₁ Cm₂) : double_nat_trans_hor_comp (id_twosided_disp_nat_trans _) (comp_hor_comp FC (identity_hor_comp _)) FC.
proof: 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 id_two_disp_left. rewrite transport_b_b_disp_mor2. use transportf_disp_mor2_eq. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor