reserve k, m, n, p, K, N for Nat;
reserve i for Integer;
reserve x, y, eps for Real;
reserve seq, seq1, seq2 for Real_Sequence;
reserve sq for FinSequence of REAL;

theorem Th17:
  for sq st len(sq)>0 holds Sum(sq)=(sq.1)+Sum(sq/^1)
proof
  let sq;
  assume
A1: len sq>0;
  then 0+1<=len sq by NAT_1:13;
  then
A2: 1 in dom sq by FINSEQ_3:25;
  thus Sum(sq) = Sum(<*sq/.1*>^(sq/^1)) by A1,CARD_1:27,FINSEQ_5:29
    .= Sum(<*sq.1*>^(sq/^1)) by A2,PARTFUN1:def 6
    .= (sq.1)+Sum(sq/^1) by RVSUM_1:76;
end;
