exact lift_naif.
exact subst_naif.
exact cumul_infer_axiom.
exact cumul_least_sort.
exact cumul_infer_rule.
exact cumul_least_prod.
exact cumul_prod.
exact cumul_inv_prod.
exact cumul_topsort_untyped.
intros.
simpl in |- *.
apply CR_WHNF_cumul_dec; auto with arith pts.
Qed.

Theorem full_cts_type_checker : PTS_TC cts_pts_functor.
Proof full_type_checker cts_pts_functor cts_prim_algos.