Proof with
try solve [simpl; destruct delta as [|p]; simpl; auto; destruct p; simpl; auto].
intros A; destruct c as [gamma delta| |]...
simpl; destruct gamma as [|p]; simpl; auto; destruct p...
remember (expr_eq e e0) as b; destruct b; simpl; try split; auto.
intro Hyp; apply A; rewrite (expr_eq_eq' _ _ Heqb); simpl; split; auto.
solve[apply var_eq_refl].
Qed.

(* Specifications: *)
Lemma ordered_factoring_sound c l0 s :
clause_denote c s -> listd clause_denote inter TT l0 s ->
listd clause_denote inter TT (ordered_factoring c l0) s.
Lemma ordered_factoring_sound c l0 s :
clause_denote c s -> listd clause_denote inter TT l0 s ->
listd clause_denote inter TT (ordered_factoring c l0) s.