reserve V for set;

theorem Th15:
  for M being non empty MetrStruct holds V in M-neighbour iff ex x
  being Element of M st V=x -neighbour
proof
  let M be non empty MetrStruct;
  V in M-neighbour implies ex x being Element of M st V=x -neighbour
  proof
    assume V in M-neighbour;
    then ex q being Subset of M st (q=V & ex x being Element of M st q=x
    -neighbour );
    hence thesis;
  end;
  hence thesis;
end;
