intros gamma work context a sound0.
apply sound_cons_gamma.
apply Derivable_Intro with (Var 0).
apply ByAssumption.
apply My_NthO.
unfold sound in |- *.
intros c in_gamma0.
elim (sound0 c in_gamma0).
intros t der_t.
apply Derivable_Intro with (Shift t).
apply ShiftIntro; assumption.
Qed.
(************************************************************)

(* Specifications: *)
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.