
theorem Lemma2a:
  for a,b being Element of [.0,1.] holds
    min (a + b, 1) in [.0,1.]
  proof
    let a,b be Element of [.0,1.];
A1: min (a + b, 1) <= 1 by XXREAL_0:17;
A2: a >= 0 & b >= 0 by XXREAL_1:1;
    min (1, a + b) = 1 or min (1, a + b) = a + b by XXREAL_0:15;
    hence thesis by A1,XXREAL_1:1,A2;
  end;
