
theorem
  for G being _Graph, T being Trail of G holds T.length() c= G.size()
proof
  let G be _Graph, T be Trail of G;
  A1: dom T.edgeSeq() = Seg len T.edgeSeq() by FINSEQ_1:def 3
    .= Seg T.length();
  rng T.edgeSeq() c= the_Edges_of G & T.edgeSeq() is one-to-one
    by GLIB_001:def 27;
  then card Seg T.length() c= card the_Edges_of G by A1, CARD_1:10;
  then card T.length() c= card the_Edges_of G by FINSEQ_1:55;
  hence thesis;
end;
