proposition: Proposition square_to_horizontal_cell_id (HB : horizontally_saturated B) {x y : B} (h : x --> y) : square_to_horizontal_cell HB (id_v_square_bicat h) = id2 h.
proof: Proof. use (invmaponpathsweq (horizontal_cell_to_square_weq HB h h)) ; cbn. rewrite square_to_horizontal_cell_to_square. rewrite horizontal_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