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
  Partial_Sums(- seq) = - Partial_Sums(seq)
proof
  Partial_Sums((-1) * seq) = (-1) * Partial_Sums(seq) by Th3;
  then Partial_Sums(- seq) = (-1) * Partial_Sums(seq) by BHSP_1:55;
  hence thesis by BHSP_1:55;
end;
