Hint Resolve DataTy_tm_subst_tm_tm DataTy_co_subst_co_tm : lngen.
(* ------------------------------------------- *)
Definition decide_Path : forall a, lc_tm a -> (exists T, Path T a) \/ (forall T, not (Path T a)).
(* ------------------------------------------- *)
(* Values and CoercedValues *)

(* Specifications: *)
Lemma tm_subst_tm_tm_Value_mutual :
(forall v,  CoercedValue v -> forall b x,  lc_tm b -> CoercedValue (tm_subst_tm_tm b x v)) /\
(forall v, Value v -> forall b x,  lc_tm b -> Value (tm_subst_tm_tm b x v)).
Lemma Value_tm_subst_tm_tm :
(forall v b x, Value v -> lc_tm b -> Value (tm_subst_tm_tm b x v)).
Lemma CoercedValue_tm_subst_tm_tm :
(forall v b x, CoercedValue v -> lc_tm b -> CoercedValue (tm_subst_tm_tm b x v)).