proposition: Lemma LL : P alpha.
proof: Proof. destruct (Zero_Limit_Succ_dec alpha). destruct s. - subst; apply PZero. - split. apply RAlim; auto. apply RBlim; auto. apply RClim; auto. apply RDlim; auto. apply RElim; auto. - destruct s; split. eapply R1;eauto. eapply RB;eauto. eapply RC;eauto. eapply RD;eauto. eapply RE;eauto. Qed.
imports: hydras(Iterates Simple_LexProd Exp2) hydras(E0 Canon Paths primRec Hprime) Coq(ArithRing Lia) Compat815 Equations(Equations) hydras(primRec)