proposition: Proposition id_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 FF) FI FI.
proof: Proof. intros x ; cbn. rewrite double_id_mor_id. rewrite id_two_disp_left. rewrite id_two_disp_right. 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