(* "le" *)

Definition counted_cmp (x y: T): SimplyProfiled bool := (1, cmp x y).

Lemma exclusive_filtering (T: Set) (p q: T -> SimplyProfiled bool) (ex: forall x, result (p x) = false \/ result (q x) = false) (l: list T): length (proj1_sig (result (filter SimplyProfiled p l))) + length (proj1_sig (result (filter SimplyProfiled q l))) <= length l.