reserve V for set;

theorem Th27:
  for M being PseudoMetricSpace, Q being Element of M-neighbour
  holds Q in elem_in_rel_2 M iff ex V being Element of M-neighbour , v being
  Element of REAL st V,Q is_dst v
proof
  let M be PseudoMetricSpace, Q be Element of M-neighbour;
  Q in elem_in_rel_2 M implies ex V being Element of M-neighbour , v being
  Element of REAL st V,Q is_dst v
  proof
    assume Q in elem_in_rel_2 M;
    then ex S being Element of M-neighbour st S=Q & ex V being Element of M
    -neighbour , v being Element of REAL st V,S is_dst v;
    hence thesis;
  end;
  hence thesis;
end;
