Neka je
![](https://static.elitesecurity.org/tex/e420b3466d9d9b9d04015825897b4ce9.png)
skup svih podskupova skupa
![](https://static.elitesecurity.org/tex/d9f12ec02412cee29506c8003a53b232.png)
koji nemaju susednih elemenata.
Svaki element bilo skupa
![](https://static.elitesecurity.org/tex/e420b3466d9d9b9d04015825897b4ce9.png)
pripada skupovima
![](https://static.elitesecurity.org/tex/17f9892c6f74e21a73940c7b8117493d.png)
i
![](https://static.elitesecurity.org/tex/7ca53b68c843207bb7fa1c3d03a2b0db.png)
. Za svaki skup
![](https://static.elitesecurity.org/tex/12d3643784bcfae78afbc12fba311c67.png)
napišimo sve skupove
![](https://static.elitesecurity.org/tex/9e1bb85380deef9adfdda9f3c4d6ebbc.png)
i
![](https://static.elitesecurity.org/tex/2819c11e4d899f61105884c65c10fdde.png)
takve da je
![](https://static.elitesecurity.org/tex/4b30c08931914d4a76dd4f6db7d9126e.png)
i
![](https://static.elitesecurity.org/tex/a301ccb63ba918d9a338e4891cc997ea.png)
. Ako
![](https://static.elitesecurity.org/tex/04386740d6ec2ed6fea5013d8203e4cc.png)
, onda je
![](https://static.elitesecurity.org/tex/ace327a3e8e417bfad6a8248c8d0a794.png)
jedini element skupa
![](https://static.elitesecurity.org/tex/17f9892c6f74e21a73940c7b8117493d.png)
koji u preseku sa skupom
![](https://static.elitesecurity.org/tex/ace327a3e8e417bfad6a8248c8d0a794.png)
daje skup
![](https://static.elitesecurity.org/tex/ace327a3e8e417bfad6a8248c8d0a794.png)
, dok u skupu
![](https://static.elitesecurity.org/tex/7ca53b68c843207bb7fa1c3d03a2b0db.png)
postoji još jedan takav skup -
![](https://static.elitesecurity.org/tex/d62423daa0eca2f24495246b7835dd6d.png)
. U slučaju kada
![](https://static.elitesecurity.org/tex/3d0f780ad99e6df6ce6d3b9fed4a2fb1.png)
onda su elementi skupa
![](https://static.elitesecurity.org/tex/17f9892c6f74e21a73940c7b8117493d.png)
koji u preseku sa skupom
![](https://static.elitesecurity.org/tex/ace327a3e8e417bfad6a8248c8d0a794.png)
daju skup
![](https://static.elitesecurity.org/tex/ace327a3e8e417bfad6a8248c8d0a794.png)
zapravo
![](https://static.elitesecurity.org/tex/ace327a3e8e417bfad6a8248c8d0a794.png)
i
![](https://static.elitesecurity.org/tex/e5b54c04105d74c17cbdfa6e3ab5e47a.png)
, dok u skupu
![](https://static.elitesecurity.org/tex/7ca53b68c843207bb7fa1c3d03a2b0db.png)
postoji još jedan takav skup -
![](https://static.elitesecurity.org/tex/d62423daa0eca2f24495246b7835dd6d.png)
. Dakle, u svakom slučaju u skupu
![](https://static.elitesecurity.org/tex/7ca53b68c843207bb7fa1c3d03a2b0db.png)
imamo po jedan takav element više nego u skupu
![](https://static.elitesecurity.org/tex/17f9892c6f74e21a73940c7b8117493d.png)
.
Kada to učinimo za sve elemente skupa
![](https://static.elitesecurity.org/tex/e420b3466d9d9b9d04015825897b4ce9.png)
, nabrojali smo sve elemente skupova
![](https://static.elitesecurity.org/tex/17f9892c6f74e21a73940c7b8117493d.png)
i
![](https://static.elitesecurity.org/tex/7ca53b68c843207bb7fa1c3d03a2b0db.png)
po jedanput. Međutim, elemenata skupa
![](https://static.elitesecurity.org/tex/7ca53b68c843207bb7fa1c3d03a2b0db.png)
ima više od elemenata skupa
![](https://static.elitesecurity.org/tex/17f9892c6f74e21a73940c7b8117493d.png)
i to tačno onoliko koliko ima elemenata skupa
![](https://static.elitesecurity.org/tex/e420b3466d9d9b9d04015825897b4ce9.png)
. Dakle,
![](https://static.elitesecurity.org/tex/cdaba54f3bc0118b86749de919f0554b.png)
.
Nije bitno koji su zaključci izvučeni, već kako se do njih došlo.