reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  0 <= (b-a)*(b+a) implies b <= -a or a <= b
proof
  assume (b-a)*(b+a)>=0;
  then b-a>=0 & b+a>=0 or b-a<=0 & b+a<=0;
  then b-a+a>=0+a or b+a<=0 by Lm6;
  then b>=0+a or b+a-a<=0-a by Lm7;
  hence thesis;
end;
