reserve a,b,i,j,k,l,m,n for Nat;

theorem SF:
  for f be nonnegative-yielding real-valued FinSequence holds
  Sum f >= Sum (f|j)
  proof
    let f be nonnegative-yielding real-valued FinSequence;
    A1: (f|j)^(f/^j) = f by RFINSEQ:8;
    Sum (f|j) + Sum (f/^j) >= Sum (f|j) + 0 by XREAL_1:6;
    hence thesis by A1,RVSUM_1:75;
  end;
