proposition: Lemma infinite_countableP E: countable_infinite E <-> (cardinal E) = aleph0.
proof: Proof. split. move => [/countableP sa /infinite_greater_countable1 sb]; apply:(cleA sa sb). move => ce; split; first by apply/countableP; rewrite - ce; fprops. apply/infinite_setP; rewrite ce; exact:CIS_aleph0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)