Nabla derivative at left-scattered

Theorem

If $f$ is continuous at $t$ and $t$ is left-scattered, then $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)},$$ where $f^{\nabla}$ denotes the nabla derivative, $\rho$ denotes the backward jump, and $\nu$ denotes the backward graininess.