Section Infer_Full_PTS.
Fixpoint full_ppal_type (t : term) :
forall e : env, wf e -> infer_ppal_type e t :=
fun e H =>
match t return (infer_ppal_type e t) with
| Srt s => infer_sort e s H
| Ref n => infer_ref e n H
| Abs A M => infer_abs full_ppal_type e A M H
| App u v => infer_app full_ppal_type e u v H
| Prod A B => infer_prod full_ppal_type e A B H
end.

Lemma tmp_add_typ : forall (e : env) (t : term), wf e -> decl_dec e (Ax t).