Instance list_forall_dec X A (p : X -> Prop) :
  (forall x, dec (p x)) -> dec (forall x, x el A -> p x).Instance list_exists_dec X A (p : X -> Prop) :
  (forall x, dec (p x)) -> dec (exists x, x el A /\ p x).

Lemma not_in_cons x y A : ~ x el y :: A -> x <> y /\ ~ x el A.