mp. apply NNF_impl_prov.
mp. apply CNF_impl_prov.
apply CNF_provable.
apply CNF_valid.
intros ? ?.
rewrite CNF_equiv_valid.
rewrite ((and_ind (fun A _ => A)) (NNF_equiv_valid v A)).
apply H;assumption.
Qed.

Theorem prov_equiv_models : forall Γ A, Γ ⊢ A <-> Γ ⊨ A.
split;[apply Soundness_general|revert A;induction Γ].