Section Filter.
Variable X : Type.
Implicit Types (x y: X) (A B C: list X) (p q: X -> bool).
Local Notation "x 'el' L" := (In x L) (at level 50).
Local Notation "A '<<=' B" := (incl A B) (at level 50).

Lemma filter_fst p x A :
p x = true -> filter p (x::A) = x::filter p A.