I solved this problem on hackerrank ( https://www.hackerrank.com/contests/dcl2k15/challenges/mice-v1 ) based on greedy approach. I am not able to understand the proof of the greedy approach.

The proof says max( |a1-b1| , |a2-b2| ) <= max( |a1-b2|, |a2-b1| ) for a1<a2 and b1<b2. Can someone help me in proving the inequality?