intros gamma work context a b der_ab sound0.
apply sound_cons_gamma.
apply der_ab.
apply sound_cons_gamma_head with gamma work; assumption.
apply sound_cons_gamma_tail with a; assumption.
Qed.

Lemma sound_cons_gamma_weak2 :
forall (gamma : flist) (work : nf_list) (context : flist) (a b c : form),
(Derivable context a -> Derivable2 context b c) ->
sound (a :: gamma) work context -> sound (b :: c :: gamma) work context.