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
  H1 : InA E.eq x0 xs
  H2 : P x0
  ============================
   (E.eq x0 x)


DEBUG:Going to execute:
fun => <coq-core.plugins.tauto::reduction_not_iff@0>