proposition: Lemma ptdlaxcommutator_genopt_nat : relativelaxcommutator_nat Mon_endo_CAT ptdlaxcommutator_genopt_data.
proof: Proof. intro Ze; induction Ze as [Z e]; intro Z'e'; induction Z'e' as [Z' e']; intro αX; induction αX as [α X]; simpl in *. apply nat_trans_eq; [apply homset_property |]; intro c; simpl. unfold BinCoproduct_of_functors_mor, BinCoproduct_of_functors_ob, δ_genoption_mor; simpl. rewrite precompWithBinCoproductArrow. rewrite postcompWithBinCoproductArrow. apply maponpaths_12. - rewrite id_left, assoc'. apply maponpaths. apply pathsinv0. rewrite <- X. apply idpath. - apply pathsinv0, nat_trans_ax. Qed.
imports: UniMath.Foundations.PartD UniMath.Combinatorics.Lists UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.ConstructionOfActegoryMorphisms UniMath.CategoryTheory.Actegories.CoproductsInActegories UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Monoidal.Examples.MonadsAsMonoidsElementary UniMath.CategoryTheory.DisplayedCats.Total UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SignatureExamples UniMath.SubstitutionSystems.SumOfSignatures UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.SubstitutionSystems UniMath.SubstitutionSystems.LiftingInitial_alt UniMath.SubstitutionSystems.MonadsFromSubstitutionSystems UniMath.SubstitutionSystems.BindingSigToMonad UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems UniMath.SubstitutionSystems.ConstructionOfGHSS UniMath.SubstitutionSystems.SigmaMonoids UniMath.SubstitutionSystems.Notation