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

theorem
  0 <= b & -a <= b implies -1 <= a/b
proof
  assume b >= 0;
  then per cases;
  suppose b = 0;
    then b" = 0;
    then a*b" = 0;
    hence thesis by XCMPLX_0:def 9;
  end;
  suppose
A2: b > 0;
    assume
A3: -a <= b;
    assume a/b < -1;
    then a/b*b < (-1)*b by A2,Lm13;
    then a < -b by A2,XCMPLX_1:87;
    hence thesis by A3,Th26;
  end;
end;
