Arguments cfind {X} A p {p_dec}.
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).

(* Specifications: *)
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.
Lemma list_exists_not_incl (X: eqType) (A B : list X) :
~ A <<= B -> exists x, x el A /\ ~ x el B.
Lemma list_cc X (p : X -> Prop) A :
(forall x, dec (p x)) ->
(exists x, x el A /\ p x) -> {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.
Lemma list_exists_not_incl (X: eqType) (A B : list X) :
~ A <<= B -> exists x, x el A /\ ~ x el B.
Lemma list_cc X (p : X -> Prop) A :
(forall x, dec (p x)) ->
(exists x, x el A /\ p x) -> {x | x el A /\ p x}.