proposition: Lemma lineator_preservesactorinv (ll : lineator_lax) : preserves_actorinv ll.
proof: Proof. intros v w x. rewrite assoc'. apply (z_iso_inv_on_right _ _ _ (z_iso_from_actor_iso Mon_V ActD _ _ _)). cbn. etrans. 2: { repeat rewrite assoc. apply cancel_postcomposition. apply lineator_preservesactor. } repeat rewrite assoc'. etrans. { apply pathsinv0, id_right. } apply maponpaths. etrans. 2: { rewrite <- functor_comp. apply maponpaths. apply pathsinv0, (actegory_actorisolaw Mon_V ActC). } apply pathsinv0, functor_id. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects