End Filtering.
(******************************************************)
(** ** Operations on lists of pairs or lists of lists *)
(******************************************************)
Section ListPairs.
Variables (A : Type) (B : Type).
(** [split] derives two lists from a list of pairs *)
Fixpoint split (l:list (A*B)) : list A * list B :=
match l with
| [] => ([], [])
| (x,y) :: tl => let (left,right) := split tl in (x::left, y::right)
end.

Lemma in_split_l : forall (l:list (A*B))(p:A*B),
In p l -> In (fst p) (fst (split l)).