Notation compatb := (Proper (E.eq==>Logic.eq)) (only parsing).

(* Specifications: *)
Lemma filter_aux_lemma: forall f s n l lo hi, searchtree lo hi s -> filter_aux f s 1%positive nil = (n,l) -> HdRel' K.lt lo l /\ Sorted K.lt l /\ S (length l) = nat_of_P n /\ (compatb f -> forall x, interp s x /\ f x = true <-> InA K.eq x l).