
theorem Wazne1:
  for z being Real st z in [.0,1.] & z <> 0 holds
    ex w being Element of [.0,1.] st w < z
  proof
    let z be Real;
    assume
A1: z in [.0,1.] & z <> 0;
    reconsider w = 0 as Element of [.0,1.] by XXREAL_1:1;
    take w;
    thus thesis by A1,XXREAL_1:1;
  end;
