reserve X for ComplexUnitarySpace;
reserve g for Point of X;
reserve seq, seq1, seq2 for sequence of X;
reserve Rseq for Real_Sequence;
reserve Cseq,Cseq1,Cseq2 for Complex_Sequence;
reserve z,z1,z2 for Complex;
reserve r for Real;
reserve k,n,m for Nat;

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 BHSP_4:def 1
    .= seq.1 + (seq.0 - seq.0) by RLVECT_1:def 3
    .= seq.1 + 09(X) by RLVECT_1:15;
  hence thesis by RLVECT_1:4;
end;
