
theorem LM080:  ::: should be somewhere
  for x being real-valued FinSequence
  st x <> {} & x is positive
  holds 0 < Sum x
  proof
    let x be real-valued FinSequence;
    assume that
    A1: x <> {} and
    A2: x is positive;
    consider i being object such that
    A3: i in dom x by A1,XBOOLE_0:def 1;
    A4: 0 < x . i by A3,A2;
    for i being Nat st i in dom x holds 0 <= x . i by A2;
    hence 0 < Sum x by RVSUM_1:85,A3,A4;
  end;
