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 S_log_square_lt_h : forall y x, y = Nat.log2 x -> 6 <= Nat.log2 x-> S y * S y <= x.