Section Removal.
Variable X : eqType.
Implicit Types x y : X.
(*  Definition neq (x : X) := decp (fun y => y <> x). *)
Definition rem A x := filter (DecPred (fun y => y <> x)) A.

Lemma rem_app' x A B C :
rem A x <<= C -> rem B x <<= C -> rem (A ++ B) x <<= C.