Definition full_type_checker : PTS_TC :=
    Build_PTS_TC (fun e t => full_ppal_type t e) check_type tmp_add_typ
      add_cst tmp_check_typ_when_wf tmp_check_wf_type.

(* Specifications: *)
Theorem decide_wf : forall e : env, decide (wf e).
Theorem decide_typ : forall (e : env) (t T : term), decide (typ e t T).