Product of delta exponentials with fixed t and s

Theorem: Let $\mathbb{T}$ be a time scale, $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be regressive functions. The following formula holds: $$e_p(t,s)e_q(t,s)=e_{p \oplus q}(t,s),$$ where $e_p$ denotes the delta exponential and $\oplus$ denotes the circle plus.

Proof: █