
theorem MaxMinIn01:
  for a,b being Element of [.0,1.] holds
    max (b, min (1-a,1-b)) in [.0,1.]
  proof
    let a,b be Element of [.0,1.];
a1: 1 - a in [.0,1.] & 1 - b in [.0,1.] by FUZNORM1:7;
    max (b, min (1-a,1-b)) = b or
      max (b, min (1-a,1-b)) = min (1-a,1-b) by XXREAL_0:16;
    hence thesis by a1,FUZNORM1:1;
  end;
