Inverse of Generator of Cyclic Group is Generator/Proof 1

Proof
Let $\gen g = G$.

Then from Set of Words Generates Group:
 * $\map W {\set {g, g^{-1} } } = G$

But:
 * $\gen {g^{-1} } = \map W {\set {g, g^{-1} } }$

and the result follows.