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 Th32:
  Sum(F1^F2) = Sum F1 + Sum F2
proof
  reconsider F3=F1,F4=F2 as FinSequence of COMPLEX by Lm2;
  thus Sum(F1^F2) = Sum(F3^F4)
    .= addcomplex.(addcomplex $$ F3,addcomplex $$ F4) by FINSOP_1:5
    .= Sum F3 + Sum F4 by BINOP_2:def 3
    .= Sum F1 + Sum F2;
end;
