proposition: Lemma countable_type_ensemble {X : Type} (S : Ensemble X) : CountableT X -> Countable S.
proof: Proof. intros. apply (inj_countable (@proj1_sig _ (In S)) H). intros [? ?] [? ?]. now apply subset_eq_compat. Qed.
imports: FiniteTypes Relation_Definitions ZArith QArith IndexedFamilies InfiniteTypes CSB DecidableDec FunctionalExtensionality ProofIrrelevance DependentTypeChoice ClassicalChoice Arith ArithRing