End Filter.
(** *** Element removal *)
Section Removal.
Variable X : eqType.
Implicit Types (x y: X) (A B: list X).
Definition rem A x : list X :=
filter (fun z => Dec (z <> x)) A.

Lemma rem_cons' A B x y :
x el B -> rem A y <<= B -> rem (x::A) y <<= B.