Zeros of delta gk

Theorem: Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $k$ be a nonnegative integer. Then for all $0 \leq n \leq k-1$, $$g_n(\rho^k(t),t)=0,$$ where $g_n$ denotes the delta gk and $\rho^k$ denotes compositions of the backward jump.

Proof: █