Goal:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  H : Forall P xs -> forall x : elt, InA E.eq x xs -> P x
  H0 : (forall x : elt, InA E.eq x xs -> P x) -> Forall P xs
  X : Prop
  ============================
   (P x /\ (forall x : elt, InA E.eq x xs -> P x) <->
    (forall x0 : elt, E.eq x0 x \/ InA E.eq x0 xs -> P x0))


DEBUG:Going to execute:
clear id0