theorem Th9:
  x1=x2 iff x1-x2=0*n
proof
  thus x1 = x2 implies x1 - x2 = 0*n by Th2;
  assume x1 - x2 = 0*n;
  hence x1 = x2 + 0*n by Th6
    .= x2 by EUCLID_4:1;
end;
