Let G be a flow network with integer edge capacities.

An edge in G is upper$-$binding if increasing its capacity by $1$ also increases the value of the maximum flow in G$.$

Similarly, an edge is lower$-$binding if decreasing its capacity by $1$ also decreases the value of the maximum flow in G$.$ Recall that an edge is saturated under a flow f if f $($e$)=$ c$($e$).$ Prove or disprove: Given a flow network G$,$ if

an edge e is saturated under a max flow f $,$ then e is an upper$-$binding edge