∀ (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],
  Field.Emb.Cardinal.leastExt F E =
    ⋯.fix fun i ih =>
      let s := Set.range fun j => (Field.Emb.Cardinal.wellOrderedBasis F E) (ih ↑j ⋯);
      ⋯.min {k | (Field.Emb.Cardinal.wellOrderedBasis F E) k ∉ IntermediateField.adjoin F s} ⋯