
theorem
  for G1, G2 being _Graph,
    F being non empty one-to-one PGraphMapping of G1, G2,
    W2 being F-valued Walk of G2
  holds
    F_V".(W2.first()) = (F"W2).first() & F_V".(W2.last()) = (F"W2).last()
  by Th127;
