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