proposition: Proposition strict_double_functor_hor_id_mor {C₁ C₂ : strict_double_cat} (F : strict_double_functor C₁ C₂) {x y : C₁} (f : x --> y) : #s F (s_id_h_square f) ⋆v id_h_to_s_square (strict_double_functor_hor_id F y) = transportf_s_square (s_id_v_left _ @ !(s_id_v_right _)) (s_id_v_left _ @ !(s_id_v_right _)) (idpath _) (idpath _) (id_h_to_s_square (strict_double_functor_hor_id F x) ⋆v s_id_h_square (#F f)).
proof: Proof. exact (is_natural_preserves_hor_id (strict_double_functor_preserves_hor_id F) f). Defined.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Examples.StrictTwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics UniMath.Bicategories.DoubleCategories.Core.CatOfStrictDoubleCats