∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : TopologicalSpace α] [inst_1 : UniformSpace β] {s : Set α}
  (G : ι → α → β) (g : α → β) (p : Filter ι)
  (motive : TendstoLocallyUniformlyOn G g p s → (x : Set α) → x ⊆ s → IsCompact x → Prop)
  (x : TendstoLocallyUniformlyOn G g p s) (x_1 : Set α) (x_2 : x_1 ⊆ s) (x_3 : IsCompact x_1),
  (∀ (h : TendstoLocallyUniformlyOn G g p s) (K : Set α) (hK1 : K ⊆ s) (hK2 : IsCompact K), motive h K hK1 hK2) →
    motive x x_1 x_2 x_3