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_eq: forall S c0 c1 c2 c3, S = (c0, (c1, (c2, c3))) -> c0 = col 0 S /\ c1 = col 1 S /\ c2 = col 2 S /\ c3 = col 3 S.