intros a context der.
elim der; clear der.
intros t der_t.
apply Derivable_Intro with (Cas a Falsum t (Var 0) (Efq (Var 0) a)).
apply OrFElim.
assumption.
apply ByAssumption.
apply My_NthO.
apply ByAbsurdity.
apply ByAssumption.
apply My_NthO.
Qed.

(* Specifications: *)
Lemma derivable_a_imp_falsum_or_b__derivable_a_imp_b :
forall (context : flist) (a b : form),
Derivable context (Imp a (OrF Falsum b)) -> Derivable context (Imp a b).