
theorem
  for a,b be positive Real holds a - b = a*b implies b is light
  proof
    let a,b be positive Real;
    b is non light implies 1/b - 1/a < 1
    proof
      assume b is non light; then
      1/b <= 1 by TA1; then
      A1: 1/b - 1/a <= 1 - 1/a by XREAL_1:9;
      1 - 1/a < 1 - 0 by XREAL_1:15;
      hence thesis by A1,XXREAL_0:2;
    end;
    hence thesis by DIO;
  end;
