∀ {α : Type u_2} {β : Type u_3} [inst : TopologicalSpace α] [inst_1 : SemilatticeSup β] [inst_2 : Zero β]
  [inst_3 : TopologicalSpace β] [inst_4 : ContinuousSup β] {ι : Type u_5} {s : Finset ι} (H : s.Nonempty)
  (f : ι → CompactlySupportedContinuousMap α β), (s.sup' H fun i => ⇑(f i)) = ⇑(s.sup' H f)