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_bijection: forall (X Y:Type) (H:FiniteT X) (g:X->Y) (Hinv:invertible g), FiniteT_nat_cardinal Y (bij_finite X Y g H Hinv) = FiniteT_nat_cardinal X H.