
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 RSSPAC2A;
    hence thesis by Def1;
  end;
