∀ {X : Type u_2} {Y : Type u_1} [inst : TopologicalSpace Y] {f : X → Y} (x : X)
  (motive : (∃ s, IsCompact s ∧ s ∈ nhds (f x)) → Prop) (x_1 : ∃ s, IsCompact s ∧ s ∈ nhds (f x)),
  (∀ (K : Set Y) (hK : IsCompact K) (hKx : K ∈ nhds (f x)), motive ⋯) → motive x_1