Prove this: In a network $(G = (V,E), u, s, t)$ with capacity set $u$, source $s$, and sink $t$, if any path from $s$ to $t$ has its value less than or equal to $\gamma$, then the maximum flow is less than or equal to $\gamma |E|$.
I am kind of confused how to start. I thought of finding the minimum cut and prove minimum cut has capacity less than or equal to $\gamma |E|$ by contradiction. Suppose not, and we will find an edge on the minimum cut with capacity strictly greater than $\gamma$, but there is no contradiction. It is perfectly okay to have an edge with capacity greater than $\gamma$. Any ideas?