Proof with simpl; auto; try solve[congruence].
induction l... intro H1.
generalize compare_clause_refl as H2; intros.
remember (rev_cmp compare_clause a c) as b; destruct b.
generalize Heqb; apply rev_cmp_eq in Heqb; rewrite Heqb.  intro Hx; apply comp_eq in Hx; auto.
right; apply IHl. generalize (in_insert_uniq _ _ _ H1) as H3.
inversion 1; subst...
right; apply IHl. generalize (in_insert_uniq _ _ _ H1) as H3.
inversion 1; subst...
Qed.
End CL_Sound.
(* some general lemmas about positives: not sure where to put these so they go here for now *)

(* Specifications: *)
Lemma positive_base_case: forall n, 0 = nat_of_P n - 1 -> n=1%positive.