Definition cartesian_to_invertible : is_invertible_2cell (α ▹ π₂). Proof. unfold is_cartesian_2cell_sfib in Hα. use make_is_invertible_2cell. - exact inv. - exact cartesian_to_invertible_map_inv. - exact cartesian_to_invertible_inv_map. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Limits.Products. Import Products.Notations.