, 1, we know that any d-SDNNF for ?(Q, I ) has size 2 ? tw(H) for some constant ? > 0 (depending only on the arity and degree bounds on I given above, which depend only on Q), which by Lemma 4.8.7 is 2 ?tw(I ) for a different constant ? > 0 and tw(I ) large enough. By definition of S k , we obtain the lower bound of 2 ?f (k) for k large enough. Now, to conclude, we must show that this lower bound also applies to any d-SDNNF for ?(Q, I)

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