proposition: Proposition enriched_eso_ff_lift_comm2_nat_trans_enrichment : nat_trans_enrichment enriched_eso_ff_lift_comm2_nat_trans (enriched_functor_enrichment (enriched_eso_ff_lift_enriched_functor · G)) (enriched_functor_enrichment Φ₂).
proof: Proof. use nat_trans_enrichment_via_comp. intros x y ; cbn. refine (!(id_right _) @ _). rewrite !assoc'. do 2 apply maponpaths. refine (!_). etrans. { apply maponpaths. rewrite !assoc. rewrite z_iso_after_z_iso_inv. apply id_left. } rewrite <- postcomp_arr_comp. rewrite <- postcomp_arr_id. apply maponpaths. apply z_iso_after_z_iso_inv. 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