Proposition enriched_eso_ff_lift_2cell_enriched_nat_trans_eq_F : F ◃ enriched_eso_ff_lift_2cell_enriched_nat_trans = τ₁. Proof. use eq_enriched_nat_trans. intro x ; cbn. refine (!_). use eq_to_iscontr_enriched_eso_ff_lift_2cell_el. pose (from_eq_enriched_nat_trans p x) as q. cbn in q. rewrite id_right, id_left in q. exact q. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.ImageEnriched. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.OrthogonalFactorization.Orthogonality. Require Import UniMath.Bicategories.OrthogonalFactorization.FactorizationSystem.