∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
  [rank_inf : Fact (Cardinal.aleph0 ≤ Module.rank F E)] [inst_3 : Algebra.IsAlgebraic F E],
  StrictMono fun x =>
    IntermediateField.adjoin F
      (⇑(Field.Emb.Cardinal.wellOrderedBasis F E) ∘ Field.Emb.Cardinal.leastExt F E '' Set.Iio x)