
theorem Lemma2:
  for a,b being Element of [.0,1.] holds
    max (0, a + b - 1) in [.0,1.]
  proof
    let a,b be Element of [.0,1.];
A1: max (0, a + b - 1) >= 0 by XXREAL_0:25;
    a <= 1 & b <= 1 by XXREAL_1:1; then
    a + b <= 1 + 1 by XREAL_1:7; then
A2: a + b - 1 <= 2 - 1 by XREAL_1:9;
    max (0, a + b - 1) = 0 or max (0, a + b - 1) = a + b - 1
      by XXREAL_0:16;
    hence thesis by A1,XXREAL_1:1,A2;
  end;
