Absolute value inequality example

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Can anyone please help me with this example from Spivak? I am math autodidact.

I have to express this without absolute value: $$a-|a-|a||$$ The answer is $$\begin{cases}a&a\ge0\\ 3a&a<0\end{cases}$$ All examples went OK, but I dont know this one. I might understand answer by intuition but I can't do it rigorously. Thanks.