Qed.
Hint Resolve erased_lc : lc.

Lemma erased_a_Abs_inversion : forall rho a,
erased_tm (a_UAbs rho a) -> forall x, x `notin` fv_tm_tm_tm a
-> erased_tm (open_tm_wrt_tm a (a_Var_f x)) /\ RhoCheck rho x (open_tm_wrt_tm a (a_Var_f x)).