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
  x0 : elt
  H2 : P x0
  H1 : E.eq x0 x
  H3 : forall y : E.t, E.eq x0 y -> impl (P x0) (P y)
  H4 : E.eq x0 x0 -> impl (P x0) (P x0)
  H5 : InA E.eq x0 xs -> P x0 -> List.Exists P xs
  ============================
   (P x)


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auto
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