Definition is_opcartesian_2cell_sopfib_inv2cell {B : bicat} {x e b : B} {p p' : e --> b} (α : invertible_2cell p p') {f g : x --> e} {β : f ==> g} (Hβ : is_opcartesian_2cell_sopfib p β) : is_opcartesian_2cell_sopfib p' β. Proof. apply is_cartesian_to_is_opcartesian_sfib. use (is_cartesian_2cell_sfib_inv2cell (inv_of_invertible_2cell (weq_op2_invertible_2cell _ _ α))). apply is_opcartesian_to_is_cartesian_sfib. exact Hβ. 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.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration.