∀ {F : Type u_1} {E : Type u_2} {K : Type u_3} [inst : Field F] [inst_1 : Field E] [inst_2 : Field K]
  [inst_3 : Algebra F E] [inst_4 : Algebra F K] (c : Set (IntermediateField.Lifts F E K)),
  IsChain (fun x1 x2 => x1 ≤ x2) c → ∃ ub, ∀ a ∈ c, a ≤ ub