for x1, x2, y1, y2, z1, z2 being object
for E being non empty set
for F being Subset of (E ^omega)
for TS being non empty transition-system over F st x1,x2 ==>* y1,y2,TS & y1,y2 ==>* z1,z2,TS holds
x1,x2 ==>* z1,z2,TS by REWRITE1:16;