
theorem Th93:
  for G1, G2 being _Graph, F being one-to-one PGraphMapping of G1, G2
  st F is onto holds card(G2.loops()) c= card(G1.loops())
proof
  let G1, G2 be _Graph, F be one-to-one PGraphMapping of G1, G2;
  reconsider F2 = F" as one-to-one PGraphMapping of G2, G1;
  assume F is onto;
  then F2 is total by Th72;
  hence thesis by Th92;
end;
