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


DEBUG:Going to execute:
fun flags =>
             <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>)