proposition: Lemma is_functional_1_I1 : is_functional_1 I1.
proof: Proof. exact (!I1_idempotent). 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