Goal:
    P : elt -> elt -> Prop  s : t
  ============================
   ((forall x : elt, In x s -> forall x0 : elt, In x0 s -> P x x0) <->
    (forall v1 v2 : elt, In v1 s -> In v2 s -> P v1 v2))


DEBUG:Going to execute:
<Coq.Init.Tauto.not_dep_intros>;
            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>)