Section SIGMA_TABLE.
Variable Site : Set.
Hypothesis eq_site_dec : eq_dec Site.
Variable LS : list Site.
(* This is generic code for any kind of tables hopefully *)
Variable Data : Set.
Let Table := Site -> Data.
Variable t : Table.
Variable s0 : Site.
Variable d0 : Data.
Variable f : Site -> Data -> Z.
(* Just an auxiliary one that is more convenient to use *)

Lemma sigma_table_change_aux :
only_once Site eq_site_dec s0 LS ->
(sigma_table Site LS Data f (update_table Site eq_site_dec Data t s0 d0) +
f s0 (t s0) - f s0 d0)%Z = sigma_table Site LS Data f t.