Abstract Algebra/Group Theory/Group/Double Inverse

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Theorem[edit]

Let G be any group with operation .

In Group G, inverse of inverse of any element g is g.

Proof[edit]

0. Choose
1. definition of inverse of g in G (usage 1,3)
2. let a = g−1
3.
4. definition of inverse of a in G (usage 2)
5. as a = g−1

Diagrams[edit]

1. inverse of filled circle is empty circle.
2. inverse of empty circle is filled circle, given 1.