∀ {α : Type u_1} {bs : List α} {x : α} {c : List α} (a : α) (as : List α)
  (motive : (∃ as', (a = x ∧ as = as') ∧ c = as' ++ bs) → Prop) (x_1 : ∃ as', (a = x ∧ as = as') ∧ c = as' ++ bs),
  (∀ (as' : List α) (aeq : a = x) (aseq : as = as') (h : c = as' ++ bs), motive ⋯) → motive x_1