theorem
  W is trivial iff W.edges() = {}
proof
  hereby
    assume W is trivial;
    then W.length() = 0;
    then W.edgeSeq() = {};
    hence W.edges() = {};
  end;
  assume W.edges() = {};
  then W.edgeSeq() = {};
  then W.length() = 0;
  hence thesis;
end;
