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 countable_sum: forall X Y:Type, CountableT X -> CountableT Y -> CountableT (X+Y).