∀ {n : ℕ} {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S],
  (∃ ι σ, ∃ (x : Finite σ) (_ : Finite ι), ∃ P, P.dimension = n) → Algebra.IsStandardSmoothOfRelativeDimension n R S