apply Clause_valid;intros v K;remember (H v K) as i eqn:x;clear x;
simpl in i;case_bool v (ClausetoPropF l).
apply IHll.
intros v K. remember (H v K). eapply proj2. apply andb_prop_elim.
rewrite <- CNF_and_valid. change (a::ll) with ([a]++ll) in H. eapply H;assumption.
assumption.
Qed.
(** Proof that if a formula in CNF is syntactically valid then it's provable*)

(* Specifications: *)
Lemma Clause_provable_3 : forall a l1 l2 Γ, In (LiteraltoPropF a) Γ -> Γ ⊢ ClausetoPropF (l1++a::l2).
intros;induction l1.