(** * Definition of prod as finType *)
Instance finTypeC_Prod (F1 F2: finType) : finTypeC (EqType (F1 * F2)).
Instance  finTypeC_Option(F: finType): finTypeC (EqType (option F)).

Lemma sum_enum_ok (X: finType) (Y: finType) x :
count (toSumList1 Y (elem X) ++ toSumList2 X (elem Y)) x = 1.