reserve V for set;

theorem
  for M being PseudoMetricSpace, v being Element of REAL, W being
Element of [:M-neighbour,M-neighbour:] holds W in ev_eq_2(v,M) iff ex V,Q being
  Element of M-neighbour st W=[V,Q] & V,Q is_dst v
proof
  let M be PseudoMetricSpace, v be Element of REAL, W be Element of [:M
  -neighbour,M-neighbour:];
  W in ev_eq_2(v,M) implies ex V,Q being Element of M-neighbour st W=[V,Q]
  & V,Q is_dst v
  proof
    assume W in ev_eq_2(v,M);
    then ex S being Element of [:M-neighbour,M-neighbour:] st W = S & ex V,Q
    being Element of M-neighbour st S=[V,Q] & V,Q is_dst v;
    hence thesis;
  end;
  hence thesis;
end;
