intros context a b der.
elim der; clear der.
intros t der_t.
apply
Derivable_Intro
with
(Abs a (Cas Falsum b (App a (Shift t) (Var 0)) (Efq (Var 0) b) (Var 0))).
apply ImpIntro.
apply OrFElim.
apply ImpElim.
apply ShiftIntro; assumption.
apply ByAssumption; apply My_NthO.
apply ByAbsurdity.
apply ByAssumption; apply My_NthO.
apply ByAssumption; apply My_NthO.
Qed.

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