
theorem Th42:
  for F1, F2 being Graph-yielding Function
  st F1, F2 are_Disomorphic holds F1, F2 are_isomorphic
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
    A2: 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;
  take p;
  thus dom p = dom F1 & rng p = dom F2 by A1;
  let x be object;
  assume x in dom F1;
  then consider G1, G2 being _Graph such that
    A3: G1 = F1.x & G2 = F2.(p.x) & G2 is G1-Disomorphic by A2;
  take G1, G2;
  thus thesis by A3;
end;
