theorem Th13: :: FSM_3:13

for X being set
for E being non empty set
for w being Element of E ^omega
for F being Subset of (E ^omega)
for TS being non empty transition-system over F
for S being Subset of TS st len w = 1 holds
( X = w -succ_of (S,TS) iff S,w ==>* X, _bool TS )