proposition: Lemma reindexed_lax_lineator_laws : lineator_laxlaws Mon_W (reindexed_actegory Mon_V ActC Mon_W U) (reindexed_actegory Mon_V ActD Mon_W U) H reindexed_lax_lineator_data.
proof: Proof. split4. - intro; intros. apply (lineator_linnatleft _ _ _ _ ll). - intro; intros. apply (lineator_linnatright _ _ _ _ ll). - intro; intros. cbn. unfold reindexed_lax_lineator_data, reindexed_actor_data. etrans. 2: { repeat rewrite assoc'. apply maponpaths. rewrite assoc. apply (lineator_preservesactor _ _ _ _ ll). } etrans. 2: { rewrite assoc. apply cancel_postcomposition. apply pathsinv0, lineator_linnatright. } etrans. 2: { rewrite assoc'. apply maponpaths. apply functor_comp. } apply idpath. - intro; intros. cbn. unfold reindexed_lax_lineator_data, reindexed_action_unitor_data. etrans. 2: { apply maponpaths. apply (lineator_preservesunitor _ _ _ _ ll). } etrans. 2: { rewrite assoc. apply cancel_postcomposition. apply pathsinv0, lineator_linnatright. } etrans. 2: { rewrite assoc'. apply maponpaths. apply functor_comp. } apply idpath. 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.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Actegories.CoproductsInActegories UniMath.CategoryTheory.Actegories.ProductsInActegories UniMath.CategoryTheory.Actegories.ProductActegory