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Since you are loading the amsmath package, you should use its environments (proof, cases, ...). Take a look at its manual.
Theorems can be setup with the amsthm package.
Thanks for the reply. After I finished typesetting this I continued with lshort and got to the part of amsthm, proof, and cases ...

Recently started learning Latex and thought it would be good practice to rewrite my math notes in latex. I got most of it down but I have trouble with formatting bits and pieces of the document. For example what command could I use to move the whole document up?
Also on the second page, the line ...