Section OrdinalPos.
Variable n' : nat.
Local Notation n := n'.+1.
Definition ord0 := Ordinal (ltn0Sn n').
Definition ord_max := Ordinal (ltnSn n').
Definition prod_finMixin := Eval hnf in FinMixin prod_enumP.
Canonical prod_finType := Eval hnf in FinType (T1 * T2) prod_finMixin.

Lemma cardX (A1 : {pred T1}) (A2 : {pred T2}) :
#|[predX A1 & A2]| = #|A1| * #|A2|.