Definition invertible_to_cartesian : is_cartesian_2cell_sfib π₁ α. Proof. intros h β δp q. use iscontraprop1. - exact (invertible_to_cartesian_unique h β δp q). - simple refine (_ ,, _ ,, _). + use binprod_ump_2cell. * apply (pr2 B). * exact δp. * exact (β ▹ _ • Hα^-1). + apply binprod_ump_2cell_pr1. + use binprod_ump_2cell_unique_alt. * apply (pr2 B). * abstract (rewrite <- !rwhisker_vcomp ; rewrite binprod_ump_2cell_pr1 ; exact (!q)). * abstract (rewrite <- !rwhisker_vcomp ; rewrite binprod_ump_2cell_pr2 ; rewrite !vassocl ; refine (_ @ id2_right _) ; rewrite vcomp_linv ; apply idpath). 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.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Limits.Products. Import Products.Notations.