Definition vcomp_is_opcartesian_2cell_sopfib {B : bicat} {e b : B} (p : e --> b) {x : B} {f g h : x --> e} {α : f ==> g} {β : g ==> h} (Hα : is_opcartesian_2cell_sopfib p α) (Hβ : is_opcartesian_2cell_sopfib p β) : is_opcartesian_2cell_sopfib p (α • β). Proof. apply is_cartesian_to_is_opcartesian_sfib. use vcomp_is_cartesian_2cell_sfib. - apply is_opcartesian_to_is_cartesian_sfib. exact Hβ. - apply is_opcartesian_to_is_cartesian_sfib. exact Hα. 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.