intros l; pattern l in |- *; apply (rev_ind (A:=Term A n)); auto.
intros x l0; case l0.
simpl in |- *.
unfold olist in |- *; simpl in |- *.
intros H' a b H'0 H'1; try assumption.
apply (d_conc _ ltM (T2M x) (T2M b) (consA (T2M a) nilA)).
generalize (olist_ltT pO); unfold ltT, olist in |- *; simpl in |- *; auto.
apply (olistOne a b); auto.
intros b l1 H' a b0 H'0; generalize H'; pattern l1 in |- *;
apply (rev_ind (A:=Term A n)); unfold ltT, olist in |- *;
simpl in |- *; auto.
intros H'2 H'3.
apply (d_conc _ ltM (T2M x) (T2M b) (consA (T2M a) (consA (T2M b0) nilA)));
auto.
generalize (olist_ltT (b0 :: nil)); unfold ltT, olist in |- *; simpl in |- *;
auto.
simpl in |- *; apply H'2; auto.
apply (desc_prefix _ ltM (consA (T2M b0) (consA (T2M b) nilA)) (T2M x)); auto.
intros x1 l2; rewrite (fP_app (l2 ++ x1 :: nil) (x :: nil));
rewrite (fP_app l2 (x1 :: nil)); rewrite (fP_app l2 (x :: nil)).
intros H'2 H'3 H'4;
apply
(d_conc _ ltM (T2M x) (T2M x1)
(consA (T2M a) (consA (T2M b0) (consA (T2M b) (fP l2))))).
generalize (olist_ltT (pX b0 (pX b l2))); unfold olist, ltT in |- *;
intros H'5; apply H'5.
rewrite (fP_app (pX b0 (pX b l2)) (pX x1 (pX x pO))); simpl in |- *; auto.
generalize (app_ass (fP l2) (consA (T2M x1) nilA) (consA (T2M x) nilA));
simpl in |- *; auto; unfold consA in |- *.
intros H'6; rewrite <- H'6; simpl in |- *; auto.
simpl in |- *; apply H'3; auto; apply (desc_prefix _ ltM) with (a := T2M x);
auto.
Qed.

Lemma fp_tail : forall x p, fP (p ++ x :: nil) = fP p ++ T2M x :: nil.
intros x p; elim p; simpl in |- *; auto.