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

theorem Th26:
  for F being FinSequence of COMPLEX,a being Element of COMPLEX
  holds Sum(a*F) = a*(Sum F)
proof
  let F be FinSequence of COMPLEX,a be Element of COMPLEX;
  set rM = multcomplex[;](a,id COMPLEX);
  thus Sum (a*F) = addcomplex $$(rM*F) by Lm1
    .= rM.(addcomplex $$F) by SEQ_4:51,54,SETWOP_2:30
    .= a*(Sum F) by Lm2;
end;
