proposition: Remark R5: exists N, forall k, N <= k -> F_ E0_omega k < F_ alpha k.
proof: Proof. destruct (F_mono_l _ _ Halpha) as [x Hx]; exists x; auto. Qed.
imports: hydras(Iterates F_alpha E0 Ack AckNotPR) Coq(ArithRing Lia Arith)