Quotient of delta exponentials with fixed t and s

Theorem

Let $\mathbb{T}$ be a time scale, $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}(\mathbb{T},\mathbb{C})$. The following formula holds: $$\dfrac{e_p(t,s;\mathbb{T})}{e_q(t,s;\mathbb{T})} = e_{p \ominus q}(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential and $\ominus$ denotes circle minus.