∀ {L : Type u_1} [inst : SemilatticeSup L] [inst_1 : TopologicalSpace L] [ContinuousSup L] {X : Type u_2}
  [inst_3 : TopologicalSpace X] {f : ℕ → X → L} {n : ℕ},
  (∀ k ≤ n, Continuous (f k)) → Continuous fun a => (partialSups fun x => f x a) n