∀ {F : Type u_2} {E : Type u_1} [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]
  {i : WithTop (Module.rank F E).ord.ToType} (x x_1 : ↑(Set.Iio i)),
  (Field.Emb.Cardinal.filtration ↑x).toSubalgebra ≤ (Field.Emb.Cardinal.filtration ↑x_1).toSubalgebra → ↑x ≤ ↑x_1