∀ {α : Type u_1} {β : Type u_2} (t : α) (ts : List α) (r : List β) (x : List α → β) (y : α) (ys : List α),
  List.permutationsAux2 t ts r (y :: ys) x =
    match List.permutationsAux2 t ts r ys fun x_1 => x (y :: x_1) with
    | (us, zs) => (y :: us, x (t :: y :: us) :: zs)