proposition: Proposition enriched_eso_ff_lift_functor_laws : is_functor enriched_eso_ff_lift_functor_data.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Subcategory.Full UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.EnrichedCats.Examples.ImageEnriched UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats UniMath.Bicategories.OrthogonalFactorization.Orthogonality UniMath.Bicategories.OrthogonalFactorization.FactorizationSystem