
theorem
  for S1, S2, S3 being Graph-membered set
  st S1, S2 are_Disomorphic & S2, S3 are_Disomorphic
  holds S1, S3 are_Disomorphic
proof
  let S1, S2, S3 be Graph-membered set;
  assume S1, S2 are_Disomorphic;
  then consider f being one-to-one Function such that
    A1: dom f = S1 & rng f = S2 and
    A2: for G being _Graph st G in S1 holds f.G is G-Disomorphic _Graph;
  assume S2, S3 are_Disomorphic;
  then consider g being one-to-one Function such that
    A3: dom g = S2 & rng g = S3 and
    A4: for G being _Graph st G in S2 holds g.G is G-Disomorphic _Graph;
  take g*f;
  thus dom(g*f) = S1 by A1, A3, RELAT_1:27;
  thus rng(g*f) = S3 by A1, A3, RELAT_1:28;
  let G be _Graph;
  assume A5: G in S1;
  then reconsider G9 = f.G as G-Disomorphic _Graph by A2;
  G9 in rng f by A1, A5, FUNCT_1:def 3;
  then g.G9 is G9-Disomorphic _Graph by A1, A4;
  hence thesis by A1, A5, FUNCT_1:13;
end;
