proposition: Proposition identity_preserves_hor_comp_laws {C : category} {D : twosided_disp_cat C C} (Cm : hor_comp D) : preserves_hor_comp_laws (identity_preserves_hor_comp_data Cm).
proof: Proof. intros x₁ x₂ y₁ y₂ z₁ z₂ vx vy vz h₁ k₁ h₂ k₂ s₁ s₂ ; cbn. rewrite id_two_disp_left, id_two_disp_right. unfold transportb_disp_mor2. rewrite transport_f_f_disp_mor2. use transportf_disp_mor2_eq. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics