The addition of natural numbers is cancellative, i.e. for all natural numbers \(x,y,z\in\mathbb N\), the following laws (both) are fulfilled:
Left cancellation property: If the equation \(z + x=z + y\) holds, then it implies \(x=y\).
Right cancellation property: If the equation \(x + z=y + z\) holds, then it implies \(x=y\).
Conversely, the equation \(x=y\) implies
for all \(x,y,z\in\mathbb N\).