proposition: Remark PA_Succ : strict_mono (H'_ alpha).
proof: Proof. destruct (Halpha beta). - subst alpha; apply Lt_Succ. - red; intros; subst alpha; repeat rewrite H'_eq2; apply PA0; auto with arith. Qed.
imports: Coq(ArithRing Lia) hydras(E0 Canon Paths) hydras(Exp2 Iterates Simple_LexProd) hydras(Compat815) Equations(Equations)