{X : Type u_4} →
  [inst : TopologicalSpace X] →
    {motive : LocPathConnectedSpace X → Sort u} →
      ((path_connected_basis : ∀ (x : X), (nhds x).HasBasis (fun s => s ∈ nhds x ∧ IsPathConnected s) id) → motive ⋯) →
        (t : LocPathConnectedSpace X) → motive t