∀ {α : Type u_1} [inst : TopologicalSpace α] {ι : Sort u_4} {δ : Type u_5} [inst_1 : CompleteLinearOrder δ]
  {f : ι → α → δ}, (∀ (i : ι), LowerSemicontinuous (f i)) → LowerSemicontinuous fun x' => ⨆ i, f i x'