Variable full_pt: parse_tree (NT (start_nt init)) full_word full_sem.
Definition init_ptd :=
match full_pt in parse_tree head full_word full_sem return
pt_zipper head full_word full_sem ->
match head return Type with | T _ => unit | NT _ => pt_dot end
with
| Terminal_pt _ _ => fun _ => ()
| Non_terminal_pt ptl =>
fun top => build_pt_dot ptl (Non_terminal_pt_ptlz top)
end Top_ptz.

Lemma init_ptd_cost:
S (ptd_cost init_ptd) = pt_size full_pt.