+lemma lstar_inv_ltransitive: ∀A,B,R. inv_ltransitive … (lstar A B R).
+#A #B #R #l1 elim l1 -l1 normalize /2 width=3/
+#a #l1 #IHl1 #l2 #b1 #b2 #H
+elim (lstar_inv_cons … b2 H ???) -H [4: // |2,3: skip ] #b #Hb1 #Hb2 (**) (* simplify line *)
+elim (IHl1 … Hb2) -IHl1 -Hb2 /3 width=3/
+qed-.
+