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