End ListDenoteSortUniqProp.
(* insert/sort uniq for preds *)
Section ListDenoteSortUniqPreds.
Context {A B : Type}.
Variables (f : A -> pred B) (b : pred B).
Variable (cmp : A -> A -> comparison).
Variable (Hcmp : forall x y, Eq = cmp x y -> x = y).
Local Hint Resolve (@interS B) (@interA B) (@unS B) (@unA B).

(* Specifications: *)
Lemma listd_insert_uniq_inter a l :
listd f inter b (insert_uniq cmp a l) = inter (f a) (listd f inter b l).
Lemma listd_sort_uniq_inter l :
listd f inter b (rsort_uniq cmp l) = listd f inter b l.
Lemma listd_insert_uniq_un a l :
listd f un b (insert_uniq cmp a l) = un (f a) (listd f un b l).
Lemma listd_sort_uniq_un l :
listd f un b (rsort_uniq cmp l) = listd f un b l.