proposition: Proposition prod_double_cat_hor_comp_laws : hor_comp_laws prod_double_cat_hor_comp_data.
proof: Proof. split. - intros. use dirprodeq ; cbn. + apply comp_h_square_id. + apply comp_h_square_id. - intros. use dirprodeq ; cbn. + apply comp_h_square_comp. + apply comp_h_square_comp. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.ProdOfTwosidedDispCat UniMath.CategoryTheory.PrecategoryBinProduct UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Core.DoubleCats UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats