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
  for n holds Sum(Cseq*seq,n+1) = (Cseq*Partial_Sums(seq)).(n+1) - Sum((
  Cseq^\1 - Cseq)*Partial_Sums(seq),n) by Th53;
