
theorem ProdGMean:
  for f,g being positive non empty real-valued FinSequence st
    len f = len g & Product f < Product g holds
      GMean f < GMean g
  proof
    let f,g be positive non empty real-valued FinSequence;
A1: Product f >= 0 & len f >= 1 by NAT_1:14;
    assume len f = len g & Product f < Product g;
    hence thesis by POWER:17,A1;
  end;
