Well-Ordering formulation correct?

[andytoh]

I looked for the most generalized lexicographical (dictionary) order on an arbitrary cartesian product in textbooks but I could not find it. So I posed my own theorem (in the form of a proof question). Is the formulation correct?

http://img409.imageshack.us/img409/5022/questionkk4.jpg

 

[andytoh]

Here's my proof. Could someone versed in set theory check if my proof is correct? I cannot find the proof in any textbook:

http://img143.imageshack.us/img143/5948/solutionbh8.jpg