∀ {A : Type u_1} (T : ↥(Descriptive.tree A)) (x y : List A) (a : A)
  (motive : y ++ [a] ∈ {y | List.take x.length y <+: x ∧ List.drop x.length y ∈ T} → Prop)
  (x_1 : y ++ [a] ∈ {y | List.take x.length y <+: x ∧ List.drop x.length y ∈ T}),
  (∀ (h1 : List.take x.length (y ++ [a]) <+: x) (h2 : List.drop x.length (y ++ [a]) ∈ T), motive ⋯) → motive x_1