reserve G for Graph,
  v, v1, v2 for Vertex of G,
  c for Chain of G,
  p, p1, p2 for Path of G,
  vs, vs1, vs2 for FinSequence of the carrier of G,
  e, X for set,
  n, m for Nat;

theorem Th4:
  e in the carrier' of G implies <*e*> is Path of G
proof
  assume e in the carrier' of G;
  then reconsider c = <*e*> as Chain of G by MSSCYC_1:5;
  now
    let n, m be Nat;
A1: len c = 1 by FINSEQ_1:39;
    assume 1 <= n & n < m & m <= len c;
    hence c.n <> c.m by A1,XXREAL_0:2;
  end;
  hence thesis by GRAPH_1:def 16;
end;
