Relationship between delta exponential and nabla exponential

Theorem: If $p$ is continuous and $\mu$-regressive then $$e_p(t,s)=\hat{e}_{\frac{p^{\rho}}{1+p^{\rho}\nu}}(t,s)=\hat{e}_{\ominus_{\nu}(-p^{\rho})}(t,s),$$ where $e_p$ denotes the $\Delta$-exponential and $\hat{e}$ denotes the $\nabla$-exponential.

Proof: █