Lemma: Equivalence of the source gain formula

For $p\in [0,1]$, the nested minimum and maximum in get_effective_gain equal (eq:gain).

Proof. If $g\le c$, the inner maximum is $c$, and the outer minimum returns $g$. If $g>c$, the interpolated value $(1-p)g+pc$ lies between $c$ and $g$, so neither operation changes it. The case $p=0$ also returns $g$.