intros gamma work context a der_a sound0.
unfold sound in |- *.
intros c in_gamma0.
elim (in_gamma_cons_gamma_rev a gamma work c in_gamma0); clear in_gamma0.
intros in_gamma0.
apply sound0; assumption.
intros eq_c;  rewrite eq_c; assumption.
Qed.

Lemma sound_cons_gamma_tail :
forall (gamma : flist) (work : nf_list) (context : flist) (a : form),
sound (a :: gamma) work context -> sound gamma work context.