∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [inst_2 : SemilatticeSup β]
  [inst_3 : ContinuousSup β] {ι : Type u_3} {s : Finset ι} (H : s.Nonempty) (f : ι → C(α, β)),
  ⇑(s.sup' H f) = s.sup' H fun i => ⇑(f i)