proposition: Lemma le_plus_l : forall alpha beta, nf alpha -> nf beta -> alpha <= beta + alpha.
proof: Proof. induction alpha. intros;apply le_zero_alpha. destruct beta. simpl;auto with T2. simpl. intros; caseEq(compare (cons beta1 beta2 0 zero) (cons alpha1 alpha2 0 zero)). intros. generalize (compare_eq_rw H1). injection 1. intros;subst beta1;subst beta2. right;constructor 6. omega. left;auto with T2. intros;right;apply psi_relevance. apply compare_gt_rw. auto with T2. Qed.
imports: EPSILON0 Arith List Omega Compare_dec Relations Wellfounded Max Tools More_nat AccP not_decreasing EPSILON0 More_nat Gamma0_prelude Gamma0_length term rpo