proposition: Lemma is_functional_2_action_abs {n : nat} (f : (L (S (S n)) : hSet)) (v : stn n → A) : is_functional_2 (aaction (abs (abs f) : ((L n) : hSet)) v).
proof: Proof. unfold is_functional_2, make_functional_2, compose, I2, aaction. rewrite <- (lift_constant_action _ _ v). rewrite (move_action_through_vector_2 A _ _ _). rewrite <- comp_action. apply (maponpaths (λ x, aaction x _)). exact (!compose_I2_abs_λ _). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.BinProducts UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Tuples UniMath.Combinatorics.Vectors UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.Algebras UniMath.AlgebraicTheories.AlgebraMorphisms UniMath.AlgebraicTheories.Examples.LambdaCalculus UniMath.AlgebraicTheories.Examples.EndomorphismTheory UniMath.AlgebraicTheories.FundamentalTheorem.SpecificUtilities.LambdaTerms UniMath.AlgebraicTheories.FundamentalTheorem.CommonUtilities.MonoidActions UniMath.AlgebraicTheories.LambdaTheories UniMath.AlgebraicTheories.LambdaCalculus UniMath.AlgebraicTheories.LambdaTheoryCategory