proposition: Proposition prod_double_cat_runitor_laws : double_runitor_laws prod_double_cat_runitor_data.
proof: Proof. intro ; intros ; cbn. rewrite transportb_twosided_disp_cat_product. use dirprodeq ; cbn. - refine (_ @ !(runitor_square _)). apply transportb_disp_mor2_eq. apply idpath. - refine (_ @ !(runitor_square _)). apply transportb_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.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