Module NatSet := FSetList.Make(OrderedTypeEx.Nat_as_OT).Infix "++" := add (at level 60, right associativity).Notation "s [=] t" := (Equal s t) (at level 70, no associativity).Module GeneralProperties := FSetProperties.Properties NatSet.

Lemma extendible_by_one:forall B', cardinal B' <= (cardinal town)-1 -> {d:elt| In d town /\ ~(In d B')}.