Goal:
  
  P : E.t -> Prop
  P_Proper : Proper (E.eq ==> impl) P
  s : t
  x : elt
  xs : list elt
  IH : Forall P xs <-> (forall x : elt, InA E.eq x xs -> P x)
  ============================
   (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:
repeat
            (match reverse goal with
             | id:?X1
               |- _ =>
                   <Coq.Init.Tauto.is_conj> flags X1; elim id; do 2 intro;
                    clear id
             | id:_ <-> _ |- _ => elim id; do 2 intro; clear id
             | id:~ _ |- _ => red in id
             | id:?X1
               |- _ =>
                   <Coq.Init.Tauto.is_disj> flags X1; elim id; intro; clear
                    id
             | _ =>
                 <Coq.Init.Tauto.find_cut>
                  ltac:(fun id0 id1 X2 =>
                          assert X2; [ exact (id0 id1) | clear id0 ])
             | id:?X1 -> ?X2
               |- _ =>
                   <Coq.Init.Tauto.is_unit_or_eq> flags X1; cut X2;
                    [ intro; clear id
                    | cut X1; [ exact id | constructor 1; fail ] ]
             | id:?X1 -> ?X2
               |- _ =>
                   <Coq.Init.Tauto.flatten_contravariant_conj> flags X1 X2 id
             | id:?X1 <-> ?X2 -> ?X3
               |- _ =>
                   assert ((X1 -> X2) -> (X2 -> X1) -> X3) by
                    (do 2 intro; apply id; split; assumption); clear id
             | id:?X1 -> ?X2
               |- _ =>
                   <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2 id
             | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; split
             | |- _ <-> _ => split
             | |- ~ _ => red
             end; <Coq.Init.Tauto.not_dep_intros>)
Level 0: Backtrace:

No matching clauses for match.