reserve V for set;

theorem Th26:
  for M being PseudoMetricSpace, V being Element of M-neighbour
  holds V in elem_in_rel_1 M iff ex Q being Element of M-neighbour , v being
  Element of REAL st V,Q is_dst v
proof
  let M be PseudoMetricSpace, V be Element of M-neighbour;
  V in elem_in_rel_1 M implies ex Q being Element of M-neighbour , v being
  Element of REAL st V,Q is_dst v
  proof
    assume V in elem_in_rel_1 M;
    then ex S being Element of M-neighbour st S=V & ex Q being Element of M
    -neighbour , v being Element of REAL st S,Q is_dst v;
    hence thesis;
  end;
  hence thesis;
end;
