proposition: Lemma disp_lhs_right_invert_cell {a b : C} {f g h : a --> b} {x : f ==> g} {y : g ==> h} {z : f ==> h} (inv_y : is_invertible_2cell y) {aa : D a} {bb : D b} {ff : aa -->[f] bb} {gg : aa -->[g] bb} {hh : aa -->[h] bb} (xx : ff ==>[x] gg) (yy : gg ==>[y] hh) (zz : ff ==>[z] hh) (H : is_disp_invertible_2cell inv_y yy) (q : x • y = z) (p := rhs_right_inv_cell _ _ _ inv_y q : x = z • inv_y^-1) (pp : xx = transportb (λ x, _ ==>[x] _) p (zz •• disp_inv_cell ((yy,,H):disp_invertible_2cell (y,,inv_y) gg hh))) : xx •• yy = transportb (λ x, _ ==>[x] _) q zz.
proof: Proof. etrans. { use (disp_lhs_right_invert_cell' _ _ _ _ pp). } apply maponpaths_2. apply cellset_property. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Univalence