proposition: Proposition enriched_eso_ff_lift_comm_eq : (enriched_eso_ff_lift_comm1_inv2cell ▹ G) • τ = rassociator _ _ _ • (F ◃ enriched_eso_ff_lift_comm2_inv2cell).
proof: 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.
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