Definition sound (Gamma : flist) (work : nf_list) (context : flist) :=
  forall a : form, in_gamma Gamma work a -> Derivable context a.

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