
theorem
  for a be Real
  for v be VECTOR of R_Algebra_of_Big_Oh_poly
  st v in negligibleFuncs
  holds a * v in negligibleFuncs
  proof
    let a be Real;
    let v be VECTOR of R_Algebra_of_Big_Oh_poly;
    assume v in negligibleFuncs;
    then
    reconsider v1=v as negligible Function of NAT,REAL by Def1;
    a(#)v1 is negligible;
    then
    a*v is negligible Function of NAT,REAL by RSSPAC3;
    hence thesis by Def1;
  end;
