Canonical prod_finType := Eval hnf in FinType (T1 * T2) prod_finMixin.

Lemma cardX (A1 : pred T1) (A2 : pred T2) : #|[predX A1 & A2]| = #|A1| * #|A2|.
Definition tag_finMixin := Eval hnf in FinMixin tag_enumP.