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 list_exists_DM X A (p : X -> Prop) : (forall x, dec (p x)) -> ~ (forall x, x el A -> ~ p x) -> exists x, x el A /\ p x.