∀ {ι : Type u} {R : Type u_1} {A : Type w} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [Nontrivial R], IsTranscendenceBasis R x → (IsEmpty ι ↔ Algebra.IsAlgebraic R A)