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.