Proof in APIO '10 P2 - Patrol

Problems and Contests
#1

[APIO '10 P2 - Patrol - DMOJ: Modern Online Judge]
Hi, I’ve read the solution of this problem but I still don’t know how to prove this highlighted text
, can anyone provide the proof (sorry for the bad English)

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#2

I got the solution from https://usaco.guide/patrol-solution.pdf#page=3