proposition: Lemma compose_compose_eq {a b c d : A} (H : a = compose c d) : compose a b = compose c (compose d b).
proof: Proof. refine (_ @ compose_assoc _ _ _). apply (maponpaths (λ x, compose x _)). exact H. 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