∀ {ι : Type u} {R : Type u_2} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  (hx : AlgebraicIndependent R x),
  hx.mvPolynomialOptionEquivPolynomialAdjoin = hx.mvPolynomialOptionEquivPolynomialAdjoin