Remark add_reduce2_1 :
 forall x y z a : Z, x = a -> (x + (y + z))%Z = (a + y + z)%Z.Remark add_reduce3 :
 forall x y z a : Z, x = a -> y = z -> (x + y)%Z = (a + z)%Z.

Lemma sigma2_sigma2_but_x_y : forall (s0 s1 : Site) (t : Table2), only_once Site eq_site_dec s0 LS1 -> only_once Site eq_site_dec s1 LS2 -> sigma2_table Site LS1 LS2 Data f t = (sigma2_but_table Site eq_site_dec LS1 LS2 Data s0 s1 f t + f s0 s1 (t s0 s1))%Z.