reserve G for Graph,
  k, m, n for Nat;

theorem Th4:
  for e being set st e in the carrier' of G holds <*e*> is directed Chain of G
proof
  let e be set;
  assume
A1: e in the carrier' of G;
  then reconsider
  s = (the Source of G).e, t = (the Target of G).e as Element of
  the carrier of G by FUNCT_2:5;
  reconsider E = the carrier' of G as non empty set by A1;
  reconsider e as Element of E by A1;
  <*s,t*> is_vertex_seq_of <*e*> by Th3;
  then reconsider c = <*e*> as Chain of G by Def1;
  c is directed
  by FINSEQ_1:39;
  hence thesis;
end;
