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:
fun flags t_reduce t_solver =>
             let rec t_tauto_intuit :=
              <Coq.Init.Tauto.simplif> flags;
               <Coq.Init.Tauto.axioms> flags ||
                 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 ||
                   match goal with
                   | |- _ -> _ => intro; t_tauto_intuit
                   | |- _ => t_reduce; t_solver
                   end || t_solver
             in
             t_tauto_intuit