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

theorem Th44:
  for F1,F2 being FinSequence of COMPLEX holds Sum(F1^F2) = Sum F1 + Sum F2
proof
  let F1,F2 be FinSequence of COMPLEX;
  thus Sum(F1^F2) = addcomplex.(addcomplex $$ F1,addcomplex $$ F2) by
FINSOP_1:5
    .= Sum F1 + Sum F2 by BINOP_2:def 3;
end;
