proposition: Lemma plus_alpha_mult_phi0 (alpha beta : Ord) (H: alpha < AP._phi0 beta) (n : nat) : alpha + mult_Sn (AP._phi0 beta) n = mult_Sn (AP._phi0 beta) n.
proof: Proof. induction n. - simpl; destruct (AP_phi0 beta ) as [ _ H1]; apply (H1 _ H). - simpl; rewrite plus_assoc; now rewrite IHn. Qed.
imports: hydras(Epsilon0.Epsilon0 ON_Generic) hydras(Schutte_basics Schutte.Addition AP CNF)