Section Set_of_tuple_of_positive.
Context {Ar : Arity}.
Fixpoint eqList (l1 l2 : list positive) :=
match l1, l2 with
| nil, nil => True
| (hd1 :: tl1), (hd2 :: tl2) => (Pos.eq hd1 hd2) /\ (eqList tl1 tl2)
| _, _ => False
end.

(* Specifications: *)
Lemma eqListRefl : forall l, eqList l l.
Lemma eqListSym : forall l l', eqList l l' -> eqList l' l.
Lemma eqListTrans : forall l1 l2 l3, eqList l1 l2 -> eqList l2 l3 -> eqList l1 l3.
Definition tST := cartesianPower positive (S (S n)).