Definition invertible_between_opcartesians {B : bicat} {x e b : B} {p : e --> b} {g₀ g₁ g₂ : x --> e} {α : g₀ ==> g₁} (Hα : is_opcartesian_2cell_sopfib p α) {β : g₀ ==> g₂} (Hβ : is_opcartesian_2cell_sopfib p β) (δ : invertible_2cell (g₂ · p) (g₁ · p)) (q : α ▹ p = (β ▹ p) • pr1 δ) : invertible_2cell g₂ g₁. Proof. use (make_invertible_2cell (weq_op2_invertible_2cell _ _ (@invertible_between_cartesians (op2_bicat B) x e b p _ _ _ α (is_opcartesian_to_is_cartesian_sfib Hα) β (is_opcartesian_to_is_cartesian_sfib Hβ) _ _))). - exact (weq_op2_invertible_2cell _ _ δ). - exact q. 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.