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

Lemma derivable_a0_and_a1_imp_b__derivable_a0_imp_a1_imp_b :
forall (a0 a1 b : form) (context : flist),
Derivable context (Imp (AndF a0 a1) b) ->
Derivable context (Imp a0 (Imp a1 b)).