- Observe that, for any
, 
This satisfies the third condition of the definition, thus proving that 
and M are isomorphic. This also completes the prove that is the minimal state DFA for L since, now, 
, ( i.e. the number of state Q in any arbitrary DFA M accepting the language L must be greater than or equal to the number of states 
of the DFA that has as states the equivalence classes of 
. )