reserve V for set;

theorem Th35:
  for M being PseudoMetricSpace, V,Q being Element of M-neighbour
  holds (nbourdist M).(V,Q) = (nbourdist M).(Q,V)
proof
  let M be PseudoMetricSpace, V,Q be Element of M-neighbour;
  consider p being Element of M such that
A1: V=p-neighbour by Th15;
  consider q being Element of M such that
A2: Q=q-neighbour by Th15;
A3: q in Q by A2,Th4;
A4: p in V by A1,Th4;
  then (nbourdist M).(V,Q) = dist(q,p) by A3,Def13
    .= (nbourdist M).(Q,V) by A4,A3,Def13;
  hence thesis;
end;
