Definition Select16Q (Q:SixteenByte) i :QuadByte :=
  match Q with (((b0, b1), b2), b3) =>
    if zeq i 0 then b0 else
    if zeq i 1 then b1 else
    if zeq i 2 then b2 else b3
  end.Definition UnSelect16Q (Q:SixteenByte) i : list QuadByte :=
  match Q with (((b0, b1), b2), b3) =>
    if zeq i 0 then [b1;b2;b3] else
    if zeq i 1 then [b0;b2;b3] else
    if zeq i 2 then [b0;b1;b3] else [b0;b1;b2]
  end.Definition SplitSelect16Q (Q:SixteenByte) i : (list QuadByte * list QuadByte) :=
  match Q with (((b0, b1), b2), b3) =>
    if zeq i 0 then ([], [b1;b2;b3]) else
    if zeq i 1 then ([b0], [b2;b3]) else
    if zeq i 2 then ([b0;b1], [b3]) else ([b0;b1;b2], [])
  end.

Lemma Select_SplitSelect16Q_Zlength Q i front back: (front, back) = SplitSelect16Q Q i -> 0<= i < 4 -> Zlength front = i /\ Zlength back = 3-i.