Proof with simpl; auto.
intros H1 H2 H3. unfold superpose. apply sp_sound... apply sp_sound...
Qed.

(* Specifications: *)
Lemma remove_trivial_atoms_sound b atms s :
listd pure_atom_denote inter b atms s ->
listd pure_atom_denote inter b (remove_trivial_atoms atms) s.
Lemma remove_trivial_atoms_equiv b atms s :
listd pure_atom_denote inter b (remove_trivial_atoms atms) s <->
listd pure_atom_denote inter b atms s.
Lemma delete_resolved_sound c s :
clause_denote c s -> clause_denote (delete_resolved c) s.