reserve i,j,n,k for Nat,
  a for Element of COMPLEX,
  R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th29:
  for F1,F2 being FinSequence of COMPLEX st len F1=len F2 holds
  Sum(F1 - F2) = Sum F1 - Sum F2
proof
  let F1,F2 be FinSequence of COMPLEX;
  assume
A1: len F1=len F2;
  reconsider y2=F2 as Element of (len F2)-tuples_on COMPLEX by FINSEQ_2:92;
  reconsider x2=F1 as Element of (len F1)-tuples_on COMPLEX by FINSEQ_2:92;
  Sum(F1 - F2) = addcomplex $$(diffcomplex.:(F1,F2)) by SEQ_4:def 7
    .= diffcomplex.(addcomplex$$x2,addcomplex$$y2) by A1,SEQ_4:51,52,def 3
,SETWOP_2:37
    .= Sum F1 - Sum F2 by BINOP_2:def 4;
  hence thesis;
end;
