
theorem
  for v,w be VECTOR of R_Algebra_of_Big_Oh_poly
  st w in negligibleFuncs
  holds v * w in negligibleFuncs
  proof
    let v,w be VECTOR of R_Algebra_of_Big_Oh_poly;
    assume w in negligibleFuncs; then
    reconsider w1=w as negligible Function of NAT,REAL by Def1;
    v in R_Algebra_of_Big_Oh_poly; then
    reconsider v1=v
    as polynomially-abs-bounded Function of NAT,REAL by LM14;
    v1(#)w1 is negligible; then
    v*w is negligible Function of NAT,REAL by RSSPAC2A;
    hence thesis by Def1;
  end;
