proposition: Lemma LModule_comp_law1 {D : category} {T : Monad C} {S : Monad C} {a : T ∙ S ⟹ S ∙ T} (l : monad_dist_laws a) (L : LModule T D) : ∏ x : C, #L (#S (η T x)) · (#L (a x) · lm_mult T L (S x)) = identity (L (S x)).
proof: Proof. intro x. now rewrite assoc, <- functor_comp, (monad_dist_law2 l), (LModule_law1 T (S x)). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.LModules