intros context i der below b.
cut (subst_form i b (Atom i) = b).
intro eq_b.
rewrite <- eq_b.
rewrite <- (subst_list_below i b context).
apply derivable_subst; assumption.
assumption.
simpl in |- *.
apply equal_dec_refl.
Qed.

Lemma derivable_weak :
forall (context : flist) (a b : form),
Derivable context a -> Derivable (b :: context) a.