proposition: Proposition square_to_vertical_cell_id (HB : vertically_saturated B) {x y : B} (v : x -|-> y) : square_to_vertical_cell HB (id_h_square_bicat v) = id2 v.
proof: Proof. use (invmaponpathsweq (vertical_cell_to_square_weq HB v v)) ; cbn. rewrite square_to_vertical_cell_to_square. rewrite vertical_cell_to_square_id. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws