(* ------------------------------------------- *)

Definition decide_Path : forall a, lc_tm a -> (exists T, Path T a) \/ (forall T, not (Path T a)).

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)).