Inductive Exists : list A -> Prop :=
      | Exists_cons_hd : forall x l, P x -> Exists (x::l)
      | Exists_cons_tl : forall x l, Exists l -> Exists (x::l).Inductive Exists : list A -> Prop :=
      | Exists_cons_hd : forall x l, P x -> Exists (x::l)
      | Exists_cons_tl : forall x l, Exists l -> Exists (x::l).Inductive Exists : list A -> Prop :=
      | Exists_cons_hd : forall x l, P x -> Exists (x::l)
      | Exists_cons_tl : forall x l, Exists l -> Exists (x::l).

Lemma incl_Exists l1 l2 : incl l1 l2 -> Exists l1 -> Exists l2.