for x, y being object
for E being non empty set
for u being Element of E ^omega
for F being Subset of (E ^omega)
for TS being non empty transition-system over F
for P being RedSequence of ==>.-relation TS st P . 1 = [x,u] & P . (len P) = [y,u] holds
for k being Nat st k in dom P holds
(P . k) `2 = u