Goal:
  
  s : VSet.t
  s' : VSet.t
  s'' : VSet.t
  i : V.t
  disj : VSet.In i s' /\ VSet.In i s'' -> False
  ininter : VSet.In i s /\ VSet.In i s''
  H : VSet.In i s -> VSet.In i s'
  ============================
   (VSet.In i s' /\ VSet.In i s'')


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 \/ ?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
             end; fold any not