reserve V for set;

theorem
  for M being PseudoMetricSpace, V,Q being Element of M-neighbour, v
  being Element of REAL holds v in ev_eq_1(V,Q) iff V,Q is_dst v
proof
  let M be PseudoMetricSpace, V,Q be Element of M-neighbour , v be Element of
  REAL;
  v in ev_eq_1(V,Q) implies V,Q is_dst v
  proof
    assume v in ev_eq_1(V,Q);
    then ex r being Element of REAL st r=v & V,Q is_dst r;
    hence thesis;
  end;
  hence thesis;
end;
