
theorem Lemma1:
  for a,b being Element of [.0,1.] holds
    a * b in [.0,1.]
  proof
    let a,b be Element of [.0,1.];
A0: 1 >= a >= 0 & 1 >= b >= 0 by XXREAL_1:1; then
    1 >= a * b by XREAL_1:160;
    hence thesis by XXREAL_1:1,A0;
  end;
