Definition max_size_image_subst (t : term) (s : variable -> value) : nat :=
  maxl (map value_size (map s (vars_of_term t))).

Lemma incl_le_max_size_image_subst : forall s t u, incl (vars_of_term t) (vars_of_term u) -> max_size_image_subst t s <= max_size_image_subst u s.