Goal:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H : List.Exists P xs -> exists x : elt, InA E.eq x xs /\ P x
  H0 : forall x : elt,
       (fun x0 : elt => InA E.eq x0 xs /\ P x0) x -> List.Exists P xs
  H1 : P x
  H2 : forall y : E.t, E.eq x y -> impl (P x) (P y)
  H3 : E.eq x x -> impl (P x) (P x)
  ============================
   (E.eq x x)


DEBUG:Going to execute:
match reverse goal with
           | id:?X1
             |- _ =>
                 <Coq.Init.Tauto.is_conj> flags X1; elim id; do 2 intro;
                  clear id
           | id:_ <-> _ |- _ => elim id; do 2 intro; clear id
           | id:~ _ |- _ => red in id
           | id:?X1
             |- _ =>
                 <Coq.Init.Tauto.is_disj> flags X1; elim id; intro; clear id
           | _ =>
               <Coq.Init.Tauto.find_cut>
                ltac:(fun id0 id1 X2 =>
                        assert X2; [ exact (id0 id1) | clear id0 ])
           | id:?X1 -> ?X2
             |- _ =>
                 <Coq.Init.Tauto.is_unit_or_eq> flags X1; cut X2;
                  [ intro; clear id
                  | cut X1; [ exact id | constructor 1; fail ] ]
           | id:?X1 -> ?X2
             |- _ =>
                 <Coq.Init.Tauto.flatten_contravariant_conj> flags X1 X2 id
           | id:?X1 <-> ?X2 -> ?X3
             |- _ =>
                 assert ((X1 -> X2) -> (X2 -> X1) -> X3) by
                  (do 2 intro; apply id; split; assumption); clear id
           | id:?X1 -> ?X2
             |- _ =>
                 <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2 id
           | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; split
           | |- _ <-> _ => split
           | |- ~ _ => red
           end; <Coq.Init.Tauto.not_dep_intros>