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_cond: forall (X:Type) (H:FiniteT X)
(n:nat),
cardinal _ (@Full_set X) n ->
FiniteT_nat_cardinal X H = n.