Proposition enriched_eso_ff_lift_functor_laws : is_functor enriched_eso_ff_lift_functor_data. Proof. split. - intro x ; cbn. use eq_to_enriched_eso_ff_lift_mor. rewrite !functor_id. rewrite id_right. rewrite z_iso_inv_after_z_iso. apply idpath. - intros x y z f g ; cbn. use eq_to_enriched_eso_ff_lift_mor. rewrite !functor_comp. rewrite !enriched_eso_ff_lift_mor_eq. rewrite !assoc'. do 2 apply maponpaths. rewrite !assoc. rewrite z_iso_after_z_iso_inv. rewrite id_left. apply idpath. 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.