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 Th40:
  Sum(R1 + R2) = Sum R1 + Sum R2
proof
  reconsider R1,R2 as i-element FinSequence of COMPLEX by FINSEQ_1:102;
  reconsider T1=R1, T2=R2 as Element of i-tuples_on COMPLEX by FINSEQ_2:131;
  Sum(R1 + R2) = addcomplex.(addcomplex$$T1,addcomplex$$T2) by SETWOP_2:35
  .= Sum R1 + Sum R2 by BINOP_2:def 3;
  hence thesis;
end;
