∀ {X : Type u_1} [inst : TopologicalSpace X] {x : X} {t : Set X} (motive : (∃ t_1 ⊆ t, IsOpen t_1 ∧ x ∈ t_1) → Prop)
  (x_1 : ∃ t_1 ⊆ t, IsOpen t_1 ∧ x ∈ t_1),
  (∀ (U : Set X) (hsub : U ⊆ t) (ho : IsOpen U) (hx : x ∈ U), motive ⋯) → motive x_1