
theorem Th57:
  for S1, S2 being vertex-disjoint GraphUnionSet
  for G1 being (GraphUnion of S1), G2 being GraphUnion of S2
  st S1,S2 are_isomorphic holds G2 is G1-isomorphic
proof
  let S1, S2 be vertex-disjoint GraphUnionSet, G1 be GraphUnion of S1;
  let G2 be GraphUnion of S2;
  assume S1,S2 are_isomorphic;
  then consider S3 being vertex-disjoint GraphUnionSet,
      E being Subset of the_Edges_of G2, G3 being GraphUnion of S3 such that
    A1: S1,S3 are_Disomorphic and
    A2: G3 is reverseEdgeDirections of G2, E by Th56;
  A3: G3 is G1-Disomorphic by A1, Th55;
  G3 is G2-isomorphic by A2, GLIBPRE0:78;
  then G2 is G3-isomorphic by GLIB_010:95;
  hence thesis by A3;
end;
