unfold CNFtoPropF at 2;unfold ClausetoPropF;simpl.
apply ImpI;apply AndI.
unfold Top;unfold Neg;apply ImpI;is_ass.
is_ass.
prov_impl_in IHll1; apply ImpI;apply AndI.
unfold CNFtoPropF;simpl;apply AndI.
eapply AndE1;is_ass.
eapply AndE1;apply K. eapply AndE2;is_ass.
eapply AndE2;apply K;eapply AndE2;is_ass.
Qed.

(* Specifications: *)
Lemma CNF_or_clause_prov : forall l1 l2, Provable (ClausetoPropF (l1++l2) → ClausetoPropF l1 ∨ ClausetoPropF l2).
intros;induction l1;simpl;unfold ClausetoPropF;simpl.