Definition tcompare (t1 t2 : tuple) :=
let (i1, i2, i3) := t1 in
let (j1, j2, j3) := t2 in
match tvcompare i1 j1 with
| Eq =>
match tvcompare i2 j2 with
| Eq => tvcompare i3 j3
|  r => r
end
|  r => r
end.

Lemma tcompare_eq t1 t2 :
match tcompare t1 t2 with Eq => t1 = t2 | _ => True end.