∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
  [inst_3 : Algebra R S] [inst_4 : Algebra S A] [inst_5 : Algebra R A] [IsScalarTower R S A],
  Function.Injective ⇑(algebraMap R S) → ∀ {x : A}, Transcendental S x → Transcendental R x