theorem
  Sum(c*F) = c*(Sum F)
proof
  reconsider F1=F as FinSequence of COMPLEX by Lm2;
  reconsider s=c as Element of COMPLEX by XCMPLX_0:def 2;
  set cM = multcomplex[;](s,id COMPLEX);
  thus Sum (c*F) = cM.(addcomplex $$ F1) by SEQ_4:51,54,SETWOP_2:30
    .= c*(Sum F1) by Lm1
    .= c*(Sum F);
end;
