Is My Proof on Images and Monotone Functions Correct?

[darkestar]

Homework Statement

Included in the pdf

Homework Equations

Included in the pdf

The Attempt at a Solution

Please take a look at pdf for my attempted solution. I would like to know how if it makes logical sense or if I should change something. Thanks!

 

[darkestar]

Any suggestions?

 

[darkestar]

Can anyone look at my proof on the attached pdf and tell me if it is correct or on the right track?