设|B|=card(B)证明:因为|A|+|B|=|A ∩B|+|A∪B|把A ∩B代入上面A ，B∩C代入上面B可得|A ∩B|+|B∩C|=|(A∪C)∩B|+|A∩C∩B|因为|(A∪C)∩B|<=|B|，|A∩C∩B|<=|A∩C|所以|(A∪C)∩B|+|A∩C∩B|<=|B|+|A∩C||A∩B|+|B∩C|<=|B|+|A∩C| 得证
