∀ {α : Type u_1} [inst : TopologicalSpace α] {ι : Sort u_4} {δ' : Type u_6}
  [inst_1 : ConditionallyCompleteLinearOrder δ'] {f : ι → α → δ'},
  (∀ (x : α), BddAbove (Set.range fun i => f i x)) →
    (∀ (i : ι), LowerSemicontinuous (f i)) → LowerSemicontinuous fun x' => ⨆ i, f i x'