proposition: Lemma action_unitor_nat_z_iso {C : category} (Act : actegory C): nat_z_iso (leftwhiskering_functor Act I_{Mon_V}) (functor_identity C).
proof: Proof. use make_nat_z_iso. - use make_nat_trans. + exact (λ x, au_{Act} x). + exact (λ x y f, actegory_unitornat Act x y f). - intro x. exists (auinv_{Act} x). apply (actegory_unitorisolaw Act x). Defined.
imports: UniMath.MoreFoundations.All UniMath.Foundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories