intuition.
eapply S_log_square_lt_h; trivial.
eapply le_trans.
2:{
eapply Nat.log2_le_mono.
eapply H.
}
rewrite Nat.log2_pow2; omega.
Qed.

Theorem log_square_lt :
forall x,
Nat.pow 2 6 <= x->
Nat.log2 x * Nat.log2 x < x.