Proof with simpl; auto.
intros; unfold normalize_atoms; rewrite listd_sort_uniq...
induction l... rewrite <-order_eqv_sound, <-IHl...
Qed.

(* Specifications: *)
Lemma list_denote_intersection_normalize_pure_atoms B l :
list_denote pure_atom_denote inter B l =
list_denote pure_atom_denote inter B (normalize_atoms l).
Lemma list_denote_union_normalize_pure_atoms B l :
list_denote pure_atom_denote un B l =
list_denote pure_atom_denote un B (normalize_atoms l).
Lemma list_denote_normalize_filter_nonreflex_atom B l :
list_denote pure_atom_denote inter B
(normalize_atoms (filter nonreflex_atom l)) =
list_denote pure_atom_denote inter B l.
Lemma order_eqv_clause_sound c s :
clause_denote (order_eqv_clause c) s <-> clause_denote c s.