proposition: Proposition transpose_strict_double_cat_hor_comp_laws : hor_comp_laws transpose_strict_double_cat_hor_comp_data.
proof: Proof. split ; cbn. - intros x y z v₁ v₂. rewrite s_id_h_square_comp. apply idpath. - intros x₁ x₂ x₃ y₁ y₂ y₃ z₁ z₂ z₃ v₁ v₁' v₂ v₂' v₃ v₃' h₁ h₂ k₁ k₂ l₁ l₂ s₁ s₁' s₂ s₂'. rewrite comp_h_square_comp. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics UniMath.Bicategories.DoubleCategories.Core.StrictDoubleCats