proposition: Fact F9 : forall i, (S n < i -> F_ beta i < F_ alpha i)%nat.
proof: Proof. intros ? ?; eapply Nat.lt_le_trans. - eapply F8;eauto. - apply F7;auto. Qed.
imports: hydras(Iterates Simple_LexProd Exp2) hydras(E0 Canon Paths primRec Hprime) Coq(ArithRing Lia) Compat815 Equations(Equations) hydras(primRec)