Proof with simpl; auto.
intros H1 H2. unfold simplify. apply delete_resolved_sound.
apply clause_denote_foldl...
intros c0 d H3 H4; apply demodulate_sound...
Qed.

Lemma space_denote_foldl
(f: list space_atom -> clause -> list space_atom) l sigma0 s :
listd clause_denote inter TT l s -> space_denote sigma0 s ->
(forall c sigma, clause_denote c s -> space_denote sigma s ->
space_denote (f sigma c) s) ->
space_denote (fold_left f l sigma0) s.