Goal:
    x : V.t  p : VSet.t  H : ~ VSet.In x p  a : V.t
  ============================
   (((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:
let dec := solve_decidable using db in
           unfold not, iff in * |-;
            repeat
             match goal with
             | H:context [ True -> False ]
               |- _ => rewrite -> Decidable.not_true_iff in H
             | H:context [ False -> False ]
               |- _ => rewrite -> Decidable.not_false_iff in H
             | H:context [ (?P -> False) -> False ]
               |- _ => rewrite -> (Decidable.not_not_iff P) in H by dec
             | H:context [ (?P -> False) -> ?Q -> False ]
               |- _ => rewrite -> (Decidable.contrapositive P Q) in H by dec
             | H:context [ (?P -> False) \/ ?Q ]
               |- _ => VSetDecide.MSetLogicalFacts.or_not_l_iff_in P Q H dec
             | H:context [ ?P \/ (?Q -> False) ]
               |- _ => VSetDecide.MSetLogicalFacts.or_not_r_iff_in P Q H dec
             | H:context [ (?P -> False) -> ?Q ]
               |- _ => rewrite -> (Decidable.imp_not_l P Q) in H by dec
             | H:context [ ?P \/ ?Q -> False ]
               |- _ => rewrite -> (Decidable.not_or_iff P Q) in H
             | H:context [ ?P /\ ?Q -> False ]
               |- _ => rewrite -> (Decidable.not_and_iff P Q) in H
             | H:context [ (?P -> ?Q) -> False ]
               |- _ => rewrite -> (Decidable.not_imp_iff P Q) in H by dec
             end; fold any not