Fixpoint lst_length (l : term_list) : nat :=
match l with
| tnil => 0
| tcons _ l' => S (lst_length l')
end.
Fixpoint term_high (t : term) : nat :=
match t with
| app a l => S (term_high_0 l)
end
with term_high_0 (l : term_list) : nat :=
match l with
| tnil => 0
| tcons hd tl => max (term_high hd) (term_high_0 tl)
end.

Lemma high_aux_2 : forall (l : term_list) (c : ad), 1 <= term_high (app c l).