we now show in the following that it satisfies all the three conditions.
- Note that, since f is a bijection,
. Also note that 
. Hence, 
. Therefore, the initial state 
of 
is mapped to the initial state 
of M thus satisfying the first condition. - We know that for any
( by definition)
(Since M accepts L)
( by definition of f )
Thus final state of
are mapped to final stat of M , satisfying the second condition.