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).