∀ {α : Type u_1} {cmp : α → α → Ordering} (c : Batteries.RBColor) (a : Batteries.RBNode α) (x : α)
  (b : Batteries.RBNode α) (path : Batteries.RBNode.Path α) (y : α)
  (motive :
    Batteries.RBNode.Path.RootOrdered cmp path y ∧
        Batteries.RBNode.OnRoot (Batteries.RBNode.cmpEq cmp y) (Batteries.RBNode.node c a x b) →
      Prop)
  (x_1 :
    Batteries.RBNode.Path.RootOrdered cmp path y ∧
      Batteries.RBNode.OnRoot (Batteries.RBNode.cmpEq cmp y) (Batteries.RBNode.node c a x b)),
  (∀ (yp : Batteries.RBNode.Path.RootOrdered cmp path y)
      (xy : Batteries.RBNode.OnRoot (Batteries.RBNode.cmpEq cmp y) (Batteries.RBNode.node c a x b)), motive ⋯) →
    motive x_1