Goal:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H0 : forall x : elt,
       (fun x0 : elt => InA E.eq x0 xs /\ P x0) x -> List.Exists P xs
  x0 : elt
  H1 : InA E.eq x0 xs
  H2 : P x0
  H3 : List.Exists P xs
  x1 : elt
  H : InA E.eq x1 xs
  H4 : P x1
  H5 : forall y : E.t, E.eq x0 y -> impl (P x0) (P y)
  ============================
   (E.eq x0 x)


DEBUG:Going to execute:
match reverse goal with
           | id:(?X1 -> ?X2) -> ?X3
             |- _ =>
                 cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | cut (X1 -> X2);
                     [ exact
                     id
                     | generalize (fun y : X2 => id (fun x : X1 => y)); intro;
                        clear id; (solve [ t_tauto_intuit ]) ] ]
           | id:~ ?X1 -> ?X3
             |- _ =>
                 cut X3;
                  [ intro; clear id; t_tauto_intuit
                  | cut (~ X1);
                     [ exact
                     id
                     | clear id; intro; (solve [ t_tauto_intuit ]) ] ]
           | |- ?X1 =>
                 <Coq.Init.Tauto.is_disj> flags X1; (solve
                  [ left; t_tauto_intuit | right; t_tauto_intuit ])
           end