intros S D rho A B H. induction H. intros. subst. exists A1, A2. auto.
intros. subst.
inversion H; subst; destruct (IHmultipar _ _ eq_refl) as [B1 [B2 EQ]]; auto;
exists B1, B2; auto.
Qed.

Lemma multipar_UAbs_Irrel : forall S D a b x,
x `notin` fv_tm_tm_tm a \u fv_tm_tm_tm b ->
multipar S D (a_UAbs Irrel a) b ->
(exists b2, b = (a_UAbs Irrel b2))
\/ (exists a1, exists a2, multipar S D (a_UAbs Irrel a) (a_UAbs Irrel a1) /\
open_tm_wrt_tm a1 (a_Var_f x) = a_App a2 Irrel a_Bullet).