{F : Type u_1} →
  [inst : Field F] →
    {K₁ : Type u_3} →
      [inst_1 : Field K₁] →
        [inst_2 : Algebra F K₁] →
          (E : Type u_6) →
            [inst_3 : Field E] →
              [inst_4 : Algebra F E] →
                [inst_5 : Algebra E K₁] → [IsScalarTower F E K₁] → [Normal F E] → Gal(K₁/F) →* Gal(E/F)