Prove the following generalizations of Prop. 3.1 (a) Let x be a capacity-feasible flow vector, and let N + and N − be two disjoint subsets of nodes. Then exactly one of the following two alternatives...

Prove the following generalizations of Prop. 3.1 (a) Let x be a capacity-feasible flow vector, and let N + and N − be two disjoint subsets of nodes. Then exactly one of the following two alternatives holds: (1) There exists a simple path that starts at some node of N +, ends at some node of N −, and is unblocked with respect to x