Goal:
  
  x : V.t
  s : VSet.t
  s' : VSet.t
  z : VSet.elt
  H : VSetProp.Add x s (VSet.remove z s')
  H0 : ~ VSet.In x s
  i : VSet.elt
  ============================
   (VSet.In i s <-> VSet.In i s /\ ~ VSet.E.eq i z)


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; Ltac.cut X2;
                     [ intro; clear id
                     | Ltac.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; Ltac.split; Ltac.assumption);
                     clear id
              | id:?X1 -> ?X2
                |- _ =>
                    <Coq.Init.Tauto.flatten_contravariant_disj> flags X1 X2
                     id
              | |- ?X1 => <Coq.Init.Tauto.is_conj> flags X1; Ltac.split
              | |- _ <-> _ => Ltac.split
              | |- ~ _ => red
              end; <Coq.Init.Tauto.not_dep_intros>)