Hint Resolve lc_tm_erase lc_brs_erase lc_constraint_erase : lc.

(* Specifications: *)
Lemma lc_tm_open_tm_wrt_tm_erase_tm : forall a,
(∀ x, lc_tm (open_tm_wrt_tm a (a_Var_f x))) ->
forall x, lc_tm (open_tm_wrt_tm (erase_tm a) (a_Var_f x)).
Lemma lc_tm_open_tm_wrt_co_erase_tm : forall a,
(∀ x, lc_tm (open_tm_wrt_co a (g_Var_f x))) ->
forall x, lc_tm (open_tm_wrt_co (erase_tm a) (g_Var_f x)).