∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (K : Type u_4)
  [inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : Algebra S K] [IsScalarTower R S K] [FaithfulSMul R S]
  [IsFractionRing S K] {x : S}, IsStronglyTranscendental R x ↔ Transcendental R ((algebraMap S K) x)