theorem
  len R1 = len R2 implies Sum (R1+R2)=Sum R1 + Sum R2
proof
  assume len R1=len R2;
  then reconsider
  r1=R1,r2=R2 as Element of (len R1)-tuples_on the carrier of V1 by FINSEQ_2:92
;
  thus Sum (R1+R2) = Sum (r1+r2) .= Sum R1+Sum R2 by FVSUM_1:76;
end;
