Section problem_knows_not_refl.
Variable town: t.
Variable n:nat.
Variable cardinality: cardinal town = 2*n+1.
Variable knows: elt -> elt -> Prop.
Variable knows_sym: forall m n, knows m n ->  knows n m.
Variable knows_extensional:forall m n p, E.eq n p -> knows m n-> knows m p.
Variable property: forall B, Subset B town -> cardinal B = n ->
{d:elt | In d (diff town B)/\(forall b, In b B -> knows d b)}.

Lemma extendible_to_n:forall B', Subset B' town -> cardinal B' <= n ->
{B:t| cardinal B = n /\  Subset B' B /\ Subset B town}.