∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α} {ι : Sort u_4} {δ : Type u_5} [inst_1 : CompleteLinearOrder δ]
  {p : ι → Prop} {f : (i : ι) → p i → α → δ},
  (∀ (i : ι) (hi : p i), UpperSemicontinuousOn (f i hi) s) →
    UpperSemicontinuousOn (fun x' => ⨅ i, ⨅ (hi : p i), f i hi x') s