reserve a, b, r, M2 for Real;
reserve Rseq,Rseq1,Rseq2 for Real_Sequence;
reserve k, n, m, m1, m2 for Nat;
reserve X for RealUnitarySpace;
reserve g for Point of X;
reserve seq, seq1, seq2 for sequence of X;

theorem
  Sum(seq, 1, 0) = seq.1
proof
  Sum(seq, 1, 0) = (seq.0 + seq.1) - Sum(seq, 0) by Th17
    .= (seq.1 + seq.0) - seq.0 by Def1
    .= seq.1 + (seq.0 - seq.0) by RLVECT_1:def 3
    .= seq.1 + 09(X) by RLVECT_1:15;
  hence thesis;
end;
