proposition: Theorem Limit_Infinity : T1limit alpha <-> (forall beta, beta t1< alpha -> Infinite (fun gamma => beta t1< gamma t1< alpha)).
proof: Proof. split; intro H. - intros beta Hbeta. exists (s beta). split. apply L3. auto. intros i; red. apply L1; auto. - specialize (L4 ); intro. apply H0. intros. destruct (H beta H1) as [x [H2 H3]]. exists (x 0). apply H3. Qed.
imports: hydras(Epsilon0 T1) Coq(Ensembles Image Compare_dec)