proposition: Lemma succ_lt_a_phi0_b : forall c a n b, c <_phi0 (cons a n b) -> succ c <_phi0 (cons a n b).
proof: Proof. induction c. - simpl; repeat constructor. - simpl; case c1. + repeat constructor. + intros t n0 t0 a n1 b H; inversion_clear H; constructor; auto. Qed.
imports: Coq(Arith Max Bool Lia Compare_dec Relations Ensembles Wellfounded Bool RelationClasses Operators_Properties ArithRing Logic.Eqdep_dec) hydras(More_Arith Restriction DecPreOrder) hydras(OrdNotations)