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 Th16:
  Sum(seq, 1) = Sum(seq, 0) + seq.1
proof
  Partial_Sums(seq).1 = Partial_Sums(seq).0 + seq.(0 + 1) by Def1
    .= Partial_Sums(seq).0 + seq.1;
  hence thesis;
end;
