
theorem DomHomogen:
  for f being heterogeneous positive non empty real-valued FinSequence holds
    dom Homogen f = dom 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;
    thus thesis by DinoDom,A1;
  end;
