
theorem
  for v,u be VECTOR of R_Algebra_of_Big_Oh_poly
  st v in negligibleFuncs & u in negligibleFuncs
  holds v + u in negligibleFuncs
  proof
    let v,u be VECTOR of R_Algebra_of_Big_Oh_poly;
    assume v in negligibleFuncs & u in negligibleFuncs; then
    reconsider v1=v,u1=u as negligible Function of NAT,REAL by Def1;
    v1+u1 is negligible; then
    v+u is negligible Function of NAT,REAL by RSSPAC2;
    hence thesis by Def1;
  end;
