
theorem
  for F1, F2 being Graph-yielding Function
  st F1, F2 are_Disomorphic holds card F1 = card F2
proof
  let F1, F2 be Graph-yielding Function;
  assume F1, F2 are_Disomorphic;
  then consider p being one-to-one Function such that
    A1: dom p = dom F1 & rng p = dom F2 and
    for x being object st x in dom F1 ex G1, G2 being _Graph
      st G1 = F1.x & G2 = F2.(p.x) & G2 is G1-Disomorphic;
  thus card F1 = card dom F1 by CARD_1:62
    .= card dom F2 by A1, CARD_1:70
    .= card F2 by CARD_1:62;
end;
