Hi guys,

I have a question about an

proof, specifically, properly handling the inequality at the end.

Prove that

Let

be given. Let

.

(1) Then

implies

(2)

implies

(3)

implies

(4)

We know that

for all

, hence (4) above implies

Now, my question involves this line. Clearly this line above is not equivalent to

, which is what we're trying to show. For my formal proof to be complete, how do I go from here?

Could I say something like:t

Is that even a true statement, and if so, is that how you do this proof?

Thanks for your help.