induction l... simpl. rewrite <-IHl. rewrite listd_insert_uniq...
Qed.
End ListDenoteInsertUniq.
(* convenience lemmas specializing insert/insert_uniq/sort/sort_uniq to and/or/ andp/orp *)
Section ListDenoteSortProp.
Context {A : Type}.
Variable (f : A -> Prop) (b : Prop).
Local Hint Resolve andS andA orS orA.

(* Specifications: *)
Lemma listd_insert_and cmp a l :
listd f and b (insert cmp a l) = and (f a) (listd f and b l).
Lemma list_sort_uniq_and l :
listd f and b (rsort_uniq cmp l) = listd f and b l.
Lemma listd_insert_uniq_or a l :
listd f or b (insert_uniq cmp a l) = or (f a) (listd f or b l).
Lemma listd_sort_uniq_or l :
listd f or b (rsort_uniq cmp l) = listd f or b l.