Proof with auto.
intros H0 H1 H2. unfold do_unfold'.
rewrite listd_app, listd_unfold_state; split. solve[apply unfolding1_sound;auto].
rewrite listd_app, listd_unfold_state; split. solve[apply unfolding2_sound;auto].
rewrite listd_app, listd_unfold_state; split. solve[apply unfolding3_sound;auto].
rewrite listd_app, listd_unfold_state; split. solve[apply unfolding4_sound;auto].
rewrite listd_app, listd_unfold_state; split. solve[apply unfolding6_sound;auto].
auto.
Qed.

Lemma listd_cong: forall l' l st,
(forall x, In x l' <-> In x l) ->
(listd clause_denote inter TT l st <-> listd clause_denote inter TT l' st).