
theorem Th10:
  for M being PseudoMetricSpace, x,p,q being Element of M holds p
  in x-neighbour & q in x-neighbour implies dist(p,q)=0
proof
  let M be PseudoMetricSpace, x,p,q be Element of M;
  assume p in x-neighbour & q in x-neighbour;
  then p tolerates x & q tolerates x by Th2;
  then p tolerates q by Th1;
  hence thesis;
end;
