HAaaa. Nick work. It'll be a pain in the arse question in some kinda math exam- proving the 'result' in the OP (prove left hand side=right hand side).
Now I start to realize the good things about being forced to do so much math in school when I was still studying in Hong Kong (which was at least 3 years ago)- I actually understand the thing and find it funny. 
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-Imagine how beautiful the world would be if we could only do things for the first-and-last time. Imagine this is the last time you would ever be able to imagine. Imagine that.
-Die Lust der Zerstörung ist gleichzeitig eine schaffende Lust.
-...and god said
Lx1,go!
and there was light...
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