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 double_log_plus_3_le_h : forall y x, y = Nat.log2 x -> y >= 4 -> 2 * y + 3 <= x.