The addition of rational Cauchy sequences is associative, i.e. for any rational Cauchy sequences \((x_n)_{n\in\mathbb N}\), \((y_n)_{n\in\mathbb N}\) and \((z_n)_{n\in\mathbb N}\) the following law is valid:
\[[(x_n)_{n\in\mathbb N}+(y_n)_{n\in\mathbb N}]+(z_n)_{n\in\mathbb N}=(x_n)_{n\in\mathbb N}+[(y_n)_{n\in\mathbb N}+(z_n)]_{n\in\mathbb N}.\]
Proofs: 1
