Hi I'm trying to prove the following proposition:Given a network $G,s,t,\omega$ where $\omega$ is the capacity, create a minimal cut cut  ${S=\left\{ (s,v)\in E_{G_{r\_max}}\right\} }$ where $G_{r\_max}$  is graph representing the the residual network(meaning we take the group of all vertices that are reachable from s in $G_{r\_max}$). So that the cut is $\left(S,V\backslash S\right)$.Given two maximal flows $f_1\neq f_2$ prove that $\left(S_1,V\backslash S_1\right)=\left(S_2,V\backslash S_2\right)$ (which are defined in the above mentioned form for each maximal flow).I've tried proving by assuming the contrary and saying that $S_1 $ is not subset of $S_2$.Tried to say that this leads to $\exists \ v\in S_1 \ \ \mbox{s.t} \ \ v\notin S_2$.Tried looking at the intersection and union of these groups but to no avail.I'd appreciate some guidance\explanation as to how best prove this claim.
Prove that every maximal flow yields the same minimal cut
graphs;network flow