
theorem
  for M being PseudoMetricSpace, p,x,y being Element of M holds p in x
  -neighbour & x tolerates y implies p in y-neighbour
proof
  let M be PseudoMetricSpace,p,x,y be Element of M;
  assume that
A1: p in x-neighbour and
A2: x tolerates y;
  p tolerates x by A1,Th2;
  then p tolerates y by A2,Th1;
  hence thesis;
end;
