∀ {F : Type u_1} [inst : Field F] (p : Polynomial F) (E : Type u_2) [inst_1 : Field E] [inst_2 : Algebra F E]
  [inst_3 : Fact (Polynomial.map (algebraMap F E) p).Splits], Function.Injective ⇑(Polynomial.Gal.galActionHom p E)