Goal:
    x : V.t  p : VSet.t  a : V.t
  ============================
   ((VSet.In a (VSet.add x (VSet.add x p)) -> VSet.In a (VSet.add x p)) /\
    (VSet.In a (VSet.add x p) -> VSet.In a (VSet.add x (VSet.add x p))))


DEBUG:Going to execute:
repeat
            match goal with
            | H:forall a : V.t, _, _:context [ VSet.In ?x _ ]
              |- _ => let P := type of (H x) in
                      assert
                      new
                      P
                      by
                      exact
                      (H x)
            | H:forall a : V.t, _
              |- context [ VSet.In ?x _ ] =>
                  let P := type of (H x) in
                  assert
                  new
                  P
                  by
                  exact
                  (H x)
            | H:forall a : V.t, _, _:context [ ?x = _ ]
              |- _ => let P := type of (H x) in
                      assert
                      new
                      P
                      by
                      exact
                      (H x)
            | H:forall a : V.t, _
              |- context [ ?x = _ ] =>
                  let P := type of (H x) in
                  assert
                  new
                  P
                  by
                  exact
                  (H x)
            | H:forall a : V.t, _, _:context [ _ = ?x ]
              |- _ => let P := type of (H x) in
                      assert
                      new
                      P
                      by
                      exact
                      (H x)
            | H:forall a : V.t, _
              |- context [ _ = ?x ] =>
                  let P := type of (H x) in
                  assert
                  new
                  P
                  by
                  exact
                  (H x)
            end;
            repeat match goal with
                   | H:forall a : V.t, _ |- _ => clear H
                   end