theorem Th7:
  c = {} implies c is cyclic
proof
  set v = the Vertex of G;
  assume c = {};
  then
A1: <*v*> is_vertex_seq_of c by GRAPH_2:32;
  <*v*>.1 = <*v*>.len <*v*> by FINSEQ_1:40;
  hence thesis by A1;
end;
