Qed.
Hint Resolve erased_lc : lc.

Lemma erased_a_Abs_exists : ∀  (rho : relflag) (a : tm) 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))
→ erased_tm (a_UAbs rho a).