Claim:
=
Proof:
means to take the union of 1( r , a )'s
for all states r that are reachable from some state
in 1*( q , w )
through zero or more arcs.
Since 1*( q , w )
is a -closure, any state reachable
from any of its states
through zero or more arcs is already in
1*( q , w ). Hence to find
all we need is to take the union of 1( r , a )'s
for all r in 1*( q , w ) , which is
.
Hence
=