∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {T₁ : CategoryTheory.Monad C} {X Y : T₁.Algebra}
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Monad.algebraFunctorOfMonadHom (CategoryTheory.CategoryStruct.id T₁)).map f)
      ((fun X =>
            CategoryTheory.Monad.Algebra.isoMk
              (CategoryTheory.Iso.refl
                ((CategoryTheory.Monad.algebraFunctorOfMonadHom (CategoryTheory.CategoryStruct.id T₁)).obj X).A)
              ⋯)
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun X =>
            CategoryTheory.Monad.Algebra.isoMk
              (CategoryTheory.Iso.refl
                ((CategoryTheory.Monad.algebraFunctorOfMonadHom (CategoryTheory.CategoryStruct.id T₁)).obj X).A)
              ⋯)
          X).hom
      ((CategoryTheory.Functor.id T₁.Algebra).map f)