proposition: Proposition double_cat_to_double_bicat_id_comp_square_laws : double_bicat_id_comp_square_laws double_cat_to_ver_bicat_sq_id_comp_whisker.
proof: Proof. repeat split. - intro ; intros ; cbn. refine (!_). apply comp_h_square_comp. - intros ; cbn. refine (!_). apply id_h_square_id. - intros ; cbn. apply comp_h_square_id. - intros ; cbn. refine (!_). apply id_h_square_comp. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.DiscreteBicat UniMath.Bicategories.DoubleCategories.DoubleBicat.Core UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Core.DoubleCats UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints UniMath.Bicategories.DoubleCategories.Underlying.HorizontalBicategory