+lemma memb_unique_append: ∀S,a,l1,l2.
+memb S a (unique_append S l1 l2) = true →
+ memb S a l1= true ∨ memb S a l2 = true.
+#S #a #l1 elim l1 normalize [#l2 #H %2 //]
+#b #tl #Hind #l2 cases (true_or_false … (a==b)) #Hab >Hab normalize /2/
+cases (memb S b (unique_append S tl l2)) normalize
+ [@Hind | >Hab normalize @Hind]
+qed.
+
+lemma unique_append_elim: ∀S:DeqSet.∀P: S → Prop.∀l1,l2.