proposition: Theorem le_inv : forall a n b a' n' b', cons a n b <= cons a' n' b' -> a < a' \/ a = a' /\ (n < n')%nat \/ a = a' /\ n = n' /\ b <= b'.
proof: Proof. intros a n b a' n' b' H; case H. injection 1; right. right; subst a; subst n ; subst b; auto with T1. intro H0; generalize (lt_inv H0). intro H1; case H1; auto. intros [(H2,H3) | (H2,(H3,H4))]. auto. right;right;auto with T1. Qed.
imports: Arith Omega Compare_dec Relations Wellfounded Tools More_nat Wf_nat AccP not_decreasing ArithRing term rpo List