proposition: Remark R0 k : H'_ (E0_phi0 3)%e0 k = iterate f (S k) k.
proof: Proof. ochange (E0_phi0 3) (E0_phi0 (E0_succ 2)); rewrite H'_Phi0_succ. unfold H'_succ_fun; apply iterate_ext. - intro x; now rewrite H'_omega_sqr. Qed.
imports: Coq(ArithRing Lia) hydras(E0 Canon Paths) hydras(Exp2 Iterates Simple_LexProd) hydras(Compat815) Equations(Equations)