Goal:
    x : V.t  p : VSet.t  H : ~ VSet.In x p  a : V.t
  ============================
   (VSet.In a (VSet.remove x (VSet.add x p)) <-> VSet.In a p)


DEBUG:Going to execute:
let dec := solve_decidable using db in
           unfold not, iff;
            repeat
             match goal with
             | |- context [ True -> False ] =>
                   rewrite -> Decidable.not_true_iff
             | |- context [ False -> False ] =>
                   rewrite -> Decidable.not_false_iff
             | |- context [ (?P -> False) -> False ] =>
                   rewrite -> (Decidable.not_not_iff P) by dec
             | |- context [ (?P -> False) -> ?Q -> False ] =>
                   rewrite -> (Decidable.contrapositive P Q) by dec
             | |- context [ (?P -> False) \/ ?Q ] =>
                   VSetDecide.MSetLogicalFacts.or_not_l_iff P Q dec
             | |- context [ ?P \/ (?Q -> False) ] =>
                   VSetDecide.MSetLogicalFacts.or_not_r_iff P Q dec
             | |- context [ (?P -> False) -> ?Q ] =>
                   rewrite -> (Decidable.imp_not_l P Q) by dec
             | |- context [ (?P -> False) /\ (?Q -> False) ] =>
                   rewrite <- (Decidable.not_or_iff P Q)
             | |- context [ ?P -> ?Q -> False ] =>
                   rewrite <- (Decidable.not_and_iff P Q)
             | |- context [ ?P /\ (?Q -> False) ] =>
                   rewrite <- (Decidable.not_imp_iff P Q) by dec
             | |- context [ (?Q -> False) /\ ?P ] =>
                   rewrite <- (Decidable.not_imp_rev_iff P Q) by dec
             end; fold any not