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

Lemma decide_Value_mutual : forall a, lc_set_tm a -> ({ Value a } + { not (Value a) }) * ({ CoercedValue a } + { not (CoercedValue a) }).