Hi guys, I just want to run this proof by you, just to see if I'm correct. I have to prove the following:

where,

Firstly, given that , and that if , then , we have that .

Secondly, pick a . Then this is such that for some , with , we have that . But, given the transitivity property, , to conclude that . Thus, .

Combining the two, we conclude that .

Thanks in advance,

HTale