
theorem HetHetero:
  for f being non empty real-valued FinSequence st
    Het f <> 0 holds f is heterogeneous
  proof
    let f be non empty real-valued FinSequence;
    assume
A1: Het f <> 0;
    assume
A3: f is homogeneous; then
    the_value_of f = Mean f by ConstantMean; then
    consider x being set such that
A2: x in dom f & Mean f = f.x by FUNCT_1:def 12,A3;
    HetSet f <> {} by A1; then
    consider y being object such that
A5: y in HetSet f by XBOOLE_0:def 1;
    consider z being Nat such that
A6: z = y & z in dom f & f.z <> Mean f by A5;
    thus thesis by A3,A2,A6;
  end;
