∀ {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} {x : X},
  (∀ k ≤ n, ContinuousAt (f k) x) → ContinuousAt (fun a => (partialSups fun x => f x a) n) x