Inductive CountableT (X:Type) : Prop :=
  | intro_nat_injection: forall f:X->nat, injective f -> CountableT X.Inductive CountableT (X:Type) : Prop :=
  | intro_nat_injection: forall f:X->nat, injective f -> CountableT X.

Lemma CountableT_is_FiniteT_or_countably_infinite: forall X:Type, CountableT X -> {FiniteT X} + {exists f:X->nat, bijective f}.