proposition: Lemma U_action_ρ_nat_trans_ok: nat_trans_data_from_nat_trans U_action_ρ_nat_trans = λ x, id x #⊗_A (strong_monoidal_functor_ϵ_inv U) · ρ_A x.
proof: Proof. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal