Regressive functions form an abelian group under circle plus

Theorem

Let $\mathbb{T}$ be a time scale. The structure $(\mathcal{R}(\mathbb{T},\mathbb{C}),\oplus_h)$ is an Abelian group, where $\mathcal{R}(\mathbb{T},\mathbb{T})$ denotes the set of regressive functions and $\oplus_h$ denotes the circle plus.