∀ {R : Type u_1} [inst : CommRing R] (X Y : ModuleCat R),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.LaxMonoidal.μ ModuleCat.equivalenceSemimoduleCat.functor X Y)
      (ModuleCat.equivalenceSemimoduleCat.functor.map (β_ X Y).hom) =
    CategoryTheory.CategoryStruct.comp
      (β_ (ModuleCat.equivalenceSemimoduleCat.functor.obj X) (ModuleCat.equivalenceSemimoduleCat.functor.obj Y)).hom
      (CategoryTheory.Functor.LaxMonoidal.μ ModuleCat.equivalenceSemimoduleCat.functor Y X)