
theorem MeanMiss:
  for f be heterogeneous non empty real-valued FinSequence holds
    MeanLess f misses MeanMore f
  proof
    let f be heterogeneous non empty real-valued FinSequence;
    assume MeanLess f meets MeanMore f; then
    consider x being object such that
A1: x in MeanLess f & x in MeanMore f by XBOOLE_0:3;
    consider i being Nat such that
A2: i = x & i in dom f & f.i < Mean f by A1;
    consider j being Nat such that
A3: j = x & j in dom f & f.j > Mean f by A1;
    thus thesis by A2,A3;
  end;
