∀ (motive : PosNum → PosNum → Sort u_1) (a b : PosNum) (h_1 : (a : PosNum) → motive a PosNum.one)
  (h_2 : (b : PosNum) → motive PosNum.one b) (h_3 : (a b : PosNum) → motive a.bit0 b.bit0)
  (h_4 : (a b : PosNum) → motive a.bit0 b.bit1) (h_5 : (a b : PosNum) → motive a.bit1 b.bit0)
  (h_6 : (a b : PosNum) → motive a.bit1 b.bit1),
  (match a.bit1, b.bit1 with
    | a, PosNum.one => h_1 a
    | PosNum.one, b => h_2 b
    | a.bit0, b.bit0 => h_3 a b
    | a.bit0, b.bit1 => h_4 a b
    | a.bit1, b.bit0 => h_5 a b
    | a.bit1, b.bit1 => h_6 a b) =
    h_6 a b