apply ImpI;eapply OrI2;is_ass.
prov_impl_in IHl1. apply ImpI. eapply OrE.
is_ass.
do 2 eapply OrI1;is_ass.
apply OrE with (ClausetoPropF l1) (ClausetoPropF l2).
apply K;is_ass.
apply OrI1;apply OrI2;is_ass.
apply OrI2;is_ass.
Qed.

Lemma CNF_add_clause_prov : forall l ll, Provable (CNFtoPropF (AddClause l ll) → ClausetoPropF l ∨ CNFtoPropF ll).
intros;induction ll;simpl;unfold CNFtoPropF;simpl.