
theorem
  for G1, G2 being VGraph, F being one-to-one PGraphMapping of G1, G2
  holds F is vlabel-preserving iff F" is vlabel-preserving
proof
  let G1, G2 be VGraph, F be one-to-one PGraphMapping of G1, G2;
  thus F is vlabel-preserving implies F" is vlabel-preserving by Th2;
  F" is vlabel-preserving implies (F")" is vlabel-preserving by Th2;
  hence thesis by Th70;
end;
