
theorem
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is Dcontinuous isomorphism holds
    (G1 is non-Dmulti iff G2 is non-Dmulti) &
    (G1 is Dsimple iff G2 is Dsimple)
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is Dcontinuous isomorphism;
  then reconsider F0 = F as one-to-one PGraphMapping of G1, G2;
  F0" is Dcontinuous isomorphism by A1, Th74, Th75;
  hence thesis by A1, Th50;
end;
