Theorem edit

Let G be any Group.

Let  

 

Proof edit

Part A.  

0. Choose  
1. Choose  
2.  
1.
3.  
closure of G,  
4.  
2,

Part B.  

5. Choose  
6.  
definition of inverse
7. Choose  
8.  
closure of G, and, y, a−1 are in G
9.  
definition of Ga
10.  
associativity on G (not Ga)
11.  
eG is identity of G
12.  

Part C.  

 
  and  ,