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;
A3: b-a>0 & b+a<0 or b-a<0 & b+a>0 by A2,Lm35;
  then
A4: b<a+0 by A1,Lm16;
  b+0<=b+a by A1,Lm6;
  then b>0-a by A1,A3,Lm17;
  hence thesis by A4;
end;
