proposition: Lemma wf_lex : forall A B eq_A_dec o1 o2, well_founded o1 -> well_founded o2 -> well_founded (lex A B eq_A_dec o1 o2).
proof: Proof. intros A B eq_A_dec o1 o2 W1 W2; unfold well_founded in *; destruct a. generalize b; clear b; pattern a; refine (well_founded_ind W1 _ _ a); clear a; intros a IH1 b; pattern b; refine (well_founded_ind W2 _ _ b). clear b; intros b IH2; apply Acc_intro. destruct y; simpl; elim (eq_A_dec a0 a); intro a0_eq_a. subst a0; apply IH2. intro; apply IH1; trivial. Qed.
imports: List more_list list_permut dickson Relations Wellfounded Arith Wf_nat term