Hint Resolve multipar_context_independent.

(* Lemma Par_iapp : forall G D a c y L, y `notin` fv_tm_tm_tm a \u L -> (forall x, x `notin` L -> RhoCheck Irrel x (open_tm_wrt_tm a (a_Var_f x))) -> Par G D (open_tm_wrt_tm a a_Bullet) c -> Par G D (a_UAbs Irrel a) (a_UAbs Irrel (close_tm_wrt_tm y c)). *)
Lemma multipar_UAbs_exists :  ∀ (x : atom) (G : context) (D : available_props)
(rho : relflag) (a a' : tm),
x `notin` fv_tm_tm_tm a
→ multipar G D (open_tm_wrt_tm a (a_Var_f x)) a'
→ multipar G D (a_UAbs rho a) (a_UAbs rho (close_tm_wrt_tm x a')).