Definition four_ints := (int * (int * (int * int)))%type.Definition col (i : Z) (s : four_ints) : int := match i with
| 0 => fst s
| 1 => fst (snd s)
| 2 => fst (snd (snd s))
| 3 => snd (snd (snd s))
| _ => Int.zero (* should not happen *)
end.

Lemma split_four_ints: forall (S: four_ints), S = (col 0 S, (col 1 S, (col 2 S, col 3 S))).