
theorem HomogenHet:
  for f be heterogeneous positive non empty real-valued FinSequence holds
    Het Homogen f < Het f
  proof
    let f be heterogeneous positive non empty real-valued FinSequence;
    consider i,j being Nat such that
A1: i = the Element of MeanLess f &
    j = the Element of MeanMore f &
    Homogen f = Replace (f, i, j, Mean f, f.i + f.j - Mean f) by HomDef;
A2: i in dom f & j in dom f & i <> j by A1,BlaBla;
    f.i <> Mean f & f.j <> Mean f by A1,BlaBla;
    hence thesis by HetMono,A1,A2;
  end;
