Definition internal_sopfib_is_opcartesian_sopfib_factor_comm : pr1 α tt · internal_sopfib_is_opcartesian_sopfib_factor = g. Proof. exact (nat_trans_eq_pointwise (is_opcartesian_2cell_sopfib_factor_comm _ Hα _ _ p) tt). Qed. Local Definition internal_sopfib_is_opcartesian_sopfib_factor_unique_help (k : pr1 G₂ tt --> z) : pr1 G₂ ⟹ Φ. Proof. use make_nat_trans. - intro x ; induction x. exact k. - abstract (intros x y f ; induction x ; induction y ; cbn ; assert (r : f = identity _) ; [ apply isapropunit | ] ; rewrite r ; rewrite !(functor_id G₂) ; rewrite id_left, id_right ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.CategoryTheory.DisplayedCats.StreetOpFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration.