I have big problem to solve, could someone help

Prove or disprove: If $\displaystyle G$ is a k-edge-connected graph and $\displaystyle v,v_{1},v_{2},...,v_{k}$ are $\displaystyle k+1$ distinct vertices of $\displaystyle G $ then for $\displaystyle i = 1,2,...k $ there exist $\displaystyle v-v_{i} $ paths $\displaystyle P_{i} $ such that each path $\displaystyle P_{i} $ contains exactly one vertex of $\displaystyle {v,v_{1},v_{2},...,v_{k}}$, namely $\displaystyle v_{i}$, and for $\displaystyle i \neq j, P_{i} $ and $\displaystyle P_{j} $ are edge-disjoint