∀ {X : Type u_1} [inst : TopologicalSpace X] {P : Set X → Set X → Prop} (c : Urysohns.CU P) (x : X) (x_1 : ℝ)
  (motive : (x_1 ∈ Set.range fun n => Urysohns.CU.approx n c x) → Prop)
  (x_2 : x_1 ∈ Set.range fun n => Urysohns.CU.approx n c x),
  (∀ (n : ℕ) (hn : (fun n => Urysohns.CU.approx n c x) n = x_1), motive ⋯) → motive x_2