proposition: Proposition structured_cospans_double_cat_functor_id_laws : double_functor_hor_id_laws structured_cospans_double_cat_functor_id_data.
proof: Proof. intros x y f. use struct_cospan_sqr_eq. rewrite transportb_disp_mor2_struct_cospan ; cbn. apply (nat_trans_ax α _ _ f). 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.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.StructuredCospans UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Preservation UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor UniMath.Bicategories.DoubleCategories.Core.DoubleCats UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats UniMath.Bicategories.DoubleCategories.Examples.StructuredCospansDoubleCat