∀ {R : Type u} {S : Type u_1} {A : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
  [inst_3 : Algebra R A] {B : Type u_2} [inst_4 : Ring B] [inst_5 : Algebra S B] {FRS : Type u_3} {FAB : Type u_4}
  [inst_6 : EquivLike FRS R S] [inst_7 : RingEquivClass FRS R S] [inst_8 : EquivLike FAB A B]
  [inst_9 : RingEquivClass FAB A B] (f : FRS) (g : FAB),
  (algebraMap S B).comp ↑f = (↑g).comp (algebraMap R A) → (Algebra.IsAlgebraic S B ↔ Algebra.IsAlgebraic R A)