∀ {R : Type u_1} (S : Type u_2) [inst : CommRing R] {A : Type u_3} [inst_1 : CommRing S] [NoZeroDivisors S]
  [inst_3 : Algebra R S] [alg : Algebra.IsAlgebraic R S] [inst_4 : Ring A] [inst_5 : Algebra R A] [inst_6 : Algebra S A]
  [IsScalarTower R S A], Function.Injective ⇑(algebraMap R A) → Function.Injective ⇑(algebraMap S A)