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:
<Coq.Init.Tauto.tauto_intuit> flags
            ltac:(<Coq.Init.Tauto.reduction_not_iff>) solver