How do you prove : a|≥ a

How do you prove a|≥ a ?

Thanks.

I don't know if this is correct formal proof, but maybe something like this:

1. a < 0 or a ≥ 0

Case I: a ≥ 0.
I.1. |a| = a (because a ≥ 0)

Case II: a < 0.
II.1. |a| = −a (because a < 0)
II.2. −a > 0 (because a < 0)
II.3. −a > a (because II.2. and a < 0)
II.4. |a| > a (because II.1. and II.3.)

2. [|a| > a and a < 0] or [|a| = a and a ≥ 0] (because I.1. and II.4.)
3. |a| > a or |a| = a (because 1. and 2.)
4. |a| ≥ a (because 3.)

QED?