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

theorem
  0 <= a & (b-a)*(b+a) <= 0 implies -a <= b & b <= a
proof
  assume that
A1: a>=0 and
A2: (b-a)*(b+a)<=0;
  b+0<=b+a by A1,Lm6;
  then b+a>=0 by A1,A2;
  then
A3: b>=0-a by Lm18;
  b-a>=0 & b+a<=0 or b-a<=0 & b+a>=0 by A2;
  then b<=a+0 by A1,Lm19;
  hence thesis by A3;
end;
