case neg =>
  replace h : K.Nonempty := Set.nonempty_iff_ne_empty.2 h
  have h2 : ContinuousOn (norm ∘ f) K := continuous_norm.comp_continuousOn hf
  have h3 : ContinuousOn (norm ∘ g) K := continuous_norm.comp_continuousOn hg
  obtain ⟨xf, _, h4⟩ : ∃ x ∈ K, ∀ y ∈ K, ‖f y‖ ≤ ‖f x‖ := hK.exists_forall_ge h h2
  obtain ⟨xg, _, h5⟩ : ∃ x ∈ K, ∀ y ∈ K, ‖g y‖ ≤ ‖g x‖ := hK.exists_forall_ge h h3
  exact hF.mul_of_bound hG h4 h5
𝕜 : Type u_1
ι : Type u_2
α : Type u_3
s K : Set α
inst✝¹ : NormedField 𝕜
F G : ι → α → 𝕜
f g : α → 𝕜
x y : 𝕜
η η' : ℝ
p : Filter ι
mf mg : ℝ
inst✝ : TopologicalSpace α
hF : TendstoUniformlyOn F f p K
hG : TendstoUniformlyOn G g p K
hf : ContinuousOn f K
hg : ContinuousOn g K
hK : IsCompact K
h : ¬K = ∅
⊢ TendstoUniformlyOn (F * G) (f * g) p K
no goals