(* liens entre PPO et sous-terme *)
Fixpoint sub_terms (t: term) : list term :=
t :: match t with
| var _ => []
| capply _ lt => flat_map sub_terms lt
| fapply _ lt => flat_map sub_terms lt
end.
Definition sub_terms_strict (t: term) : list term :=
match t with
| var _ => []
| capply _ lt => flat_map sub_terms lt
| fapply _ lt => flat_map sub_terms lt
end.

Lemma sub_term_le_size (t1 t2: term) :
In t1 (sub_terms t2) -> t2 = t1 \/ term_size t1 < term_size t2.