
theorem Th12:
  for M being non empty MetrSpace,x,y being Element of M holds y
  in x-neighbour iff y = x
proof
  let M be non empty MetrSpace, x,y be Element of M;
  hereby
    assume y in x-neighbour;
    then ex q be Element of M st y = q & x tolerates q;
    hence y = x by Th11;
  end;
  assume y = x;
  then x tolerates y by Th11;
  hence thesis;
end;
