exact prod_mem_prod (mem_principal_self s) univ_mem
case refine_1
α : Type u_1
ι : Type u_2
E : Type u_3
F : Type u_4
s : Set ι
inst✝² : TopologicalSpace ι
C : ι → E
c : F
inst✝¹ : NormedAddGroup E
inst✝ : SeminormedAddGroup F
hf : ContinuousOn C s
hs : IsCompact s
hC : ∀ i ∈ s, C i ≠ 0
l : Filter α
⊢ s ×ˢ Set.univ ∈ 𝓟 s ×ˢ l
no goals