Forward circle minus

Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the Hilger complex plane. We define the $\ominus_h$ operation by $$\ominus_h z = \dfrac{-z}{1+zh}.$$

Properties

Theorem

The circle minus $\ominus_h$ is the inverse operation of the circle plus operation $\oplus_h$. Moreover, $$z \ominus_h w = z \oplus_h (\ominus_h w).$$