
theorem ConstantGMean:
  for f being non empty constant positive real-valued FinSequence holds
    GMean f = the_value_of f
  proof
    let f be non empty constant positive real-valued FinSequence;
    reconsider v = the_value_of f as Real;
A3: len f >= 1 by NAT_1:14;
A4: v >= 0 by PosLeq;
    Product f = v |^ (len f) by ConstantProduct;
    hence thesis by A4,A3,POWER:4;
  end;
