Proposition enriched_eso_ff_lift_comm_eq : (enriched_eso_ff_lift_comm1_inv2cell ▹ G) • τ = rassociator _ _ _ • (F ◃ enriched_eso_ff_lift_comm2_inv2cell). Proof. use eq_enriched_nat_trans. intros x ; cbn. rewrite id_left. refine (_ @ id_right _). refine (!_). etrans. { apply maponpaths. exact (!(z_iso_after_z_iso_inv (nat_z_iso_pointwise_z_iso τ_iso x))). } rewrite !assoc. apply maponpaths_2. refine (!_). exact (enriched_eso_ff_lift_comm1_nat_trans_data_eq x). 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.