Ltac eauto_lc :=
eauto using lc_tm_of_lc_set_tm,
lc_co_of_lc_set_co,
lc_constraint_of_lc_set_constraint.

Lemma binds_dec_ax : forall x G, {A, B | binds x (Ax A B) G} + {(forall A B, ¬ binds x (Ax A B) G)}.
Definition rho_eq_dec : forall rho rho' : relflag, {rho = rho'} + {rho <> rho'}.