proposition: Lemma countable_Gamma_0: countable_ordinal Gamma_0.
proof: Proof. have sa:= CIS_omega. have sb:= Sphi_p5. have sc:= (cnext_zero sa). have sd: (forall x, inc x aleph_one -> inc ((Sphi^~ \0o) x) aleph_one). by move => x xa; apply:Sphi_bounded. by move /aleph_oneP: (next_fix_point_small sa sb sd sc). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)