∀ {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],
  IsTranscendenceBasis R x → ∀ {t : Set A}, Set.range x = t → IsTranscendenceBasis R Subtype.val