theorem Th51:
  {} in G-CycleSet
proof
  reconsider p = {} as Path of G by GRAPH_1:14;
  set v = the Vertex of G;
  <*v*> is_vertex_seq_of p & <*v*>.1 = <*v*>.len <*v*> by FINSEQ_1:40;
  then p is cyclic;
  hence thesis by Def8;
end;
