∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {α : E},
  IsIntegral F α →
    Function.Bijective
      ⇑(AdjoinRoot.liftAlgHom (minpoly F α) (Algebra.ofId F ↥F⟮α⟯) (IntermediateField.AdjoinSimple.gen F α) ⋯)