
theorem LukaIn01:
  for a,b being Element of [.0,1.] holds
    min (1,1-a+b) in [.0,1.]
  proof
    let a,b be Element of [.0,1.];
A1: min (1, 1-a+b) <= 1 by XXREAL_0:17;
    1 - a in [.0,1.] by FUZNORM1:7; then
    1 - a >= 0 & b >= 0 by XXREAL_1:1; then
    min (1, 1-a+b) >= 0 by XXREAL_0:20;
    hence thesis by A1,XXREAL_1:1;
  end;
