Definition is_opcartesian_to_is_cartesian_sfib {B : bicat} {e b : B} {p : e --> b} {x : B} {f g : x --> e} {α : f ==> g} (Hα : is_opcartesian_2cell_sopfib p α) : @is_cartesian_2cell_sfib (op2_bicat B) e b p x g f α. Proof. intros h γ δp q. use iscontraprop1. - abstract (use invproofirrelevance ; intros δ₁ δ₂ ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; exact (is_opcartesian_2cell_sopfib_factor_unique _ Hα _ γ δp q _ _ (pr12 δ₁) (pr12 δ₂) (pr22 δ₁) (pr22 δ₂))). - exact (is_opcartesian_2cell_sopfib_factor _ Hα γ δp q ,, is_opcartesian_2cell_sopfib_factor_over _ Hα _ _ q ,, is_opcartesian_2cell_sopfib_factor_comm _ Hα _ _ 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.