Definition negligible(f : nat -> Rat) :=
  forall c, exists n, forall x (pf_nz : nz x),
    x > n ->
    ~ ((1 / expnat x c) <= f x)%rat.

Theorem negligible_const_mult : forall (n : nat) d f, negligible f -> negligible (fun x => (RatIntro n d) * (f x))%rat.