Proof with simpl; auto.
intros H1 H2 H3. revert c0 H2. induction l... intros c0 H2.
inversion H1; apply IHl...
Qed.

Lemma simplify_sound l c s :
listd clause_denote inter TT l s -> clause_denote c s ->
clause_denote (simplify l c) s.