Definition FiniteT_nat_cardinal (X:Type) (H:FiniteT X) : nat :=
  proj1_sig (constructive_definite_description _
              (FiniteT_has_nat_cardinal X H)).

Lemma FiniteT_nat_cardinal_option: forall (X:Type) (H:FiniteT X), FiniteT_nat_cardinal (option X) (add_finite X H) = S (FiniteT_nat_cardinal X H).