
theorem
  for F1, F2 being non empty Graph-yielding Function
  for S1 being GraphSum of F1, S2 being GraphSum of F2
  st F1, F2 are_isomorphic holds S2 is S1-isomorphic
proof
  let F1, F2 be non empty Graph-yielding Function;
  let S1 be GraphSum of F1, S2 be GraphSum of F2;
  set C1 = canGFDistinction(F1), C2 = canGFDistinction(F2);
  set T1 = (the GraphUnion of rng C1), T2 = the GraphUnion of rng C2;
  assume F1,F2 are_isomorphic;
  then C1, C2 are_isomorphic by Th89;
  then A1: T2 is T1-isomorphic by Th57, Th75;
  A2: S1 is T1-Disomorphic & S2 is T2-Disomorphic by Th116;
  then S1 is T1-isomorphic;
  then T1 is S1-isomorphic by GLIB_010:95;
  hence thesis by A1, A2;
end;
