∀ (R : Type u) (A : Type v) [inst : CommRing R] [IsDomain R] [inst_2 : CommRing A] [IsDomain A] [inst_4 : Algebra R A]
  [Module.IsTorsionFree R A] [Infinite R],
  Cardinal.lift.{u, v} (Cardinal.mk { x // IsAlgebraic R x }) = Cardinal.lift.{v, u} (Cardinal.mk R)