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