
theorem
  for X be RealLinearSpace,
      R1, R2 be FinSequence of X
    st len R1 = len R2 holds Sum(R1+R2) = Sum(R1) + Sum(R2)
proof
  let X be RealLinearSpace,
      R1, R2 be FinSequence of X;
  assume len R1 = len R2; then
  dom R1 = dom R2 by FINSEQ_3:29;
  hence thesis by BINOM:7;
end;
