proposition: Proposition square_to_vertical_cell_comp (HB : vertically_saturated B) {x y : B} {v₁ v₂ v₃ : x -|-> y} (s₁ : square_double_bicat (id_h x) (id_h y) v₁ v₂) (s₂ : square_double_bicat (id_h x) (id_h y) v₂ v₃) : square_to_vertical_cell HB (comp_ver_globular_square s₁ s₂) = square_to_vertical_cell HB s₁ • square_to_vertical_cell HB s₂.
proof: Proof. use (invmaponpathsweq (vertical_cell_to_square_weq HB v₁ v₃)) ; cbn. rewrite vertical_cell_to_square_comp. rewrite !square_to_vertical_cell_to_square. 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