reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

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;
