Goal:
    x : V.t  p : VSet.t  H : ~ VSet.In x p  a : V.t  H1 : x = a \/ x <> a
  ============================
   (((x = a \/ VSet.In a p) /\ x <> a -> VSet.In a p) /\
    (VSet.In a p -> (x = a \/ VSet.In a p) /\ x <> a))


DEBUG:Going to execute:
<Coq.Init.Tauto.not_dep_intros>
Level 2: evaluation returns
<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>)
where
flags := 
of type
tauto_flags of type tacvalue