Semigroup property of delta exponential

Theorem: Let $\mathbb{T}$ be a time scale, $t,s \in \mathbb{T}$, and let $\in \mathcal{R}\left( \mathbb{T},\mathbb{C} \right)$ be regressive. the following formula holds: $$e_p(t,r;\mathbb{T})e_p(r,s;\mathbb{T})=e_p(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential.

Proof: █