
theorem Wazne2:
  for z being Real st z in [.0,1.] & z <> 1 holds
    ex w being Element of [.0,1.] st w > z
  proof
    let z be Real;
    assume
A1: z in [.0,1.] & z <> 1;
    reconsider w = 1 as Element of [.0,1.] by XXREAL_1:1;
    take w;
    1 >= z by A1,XXREAL_1:1;
    hence thesis by A1,XXREAL_0:1;
  end;
