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
  vs is_vertex_seq_of c implies for n being Element of NAT st n in dom c
  holds (vs.n = (the Target of G).(c.n) & vs.(n+1) = (the Source of G).(c.n) or
  vs.n = (the Source of G).(c.n) & vs.(n+1) = (the Target of G).(c.n))
proof
  assume
A1: vs is_vertex_seq_of c;
  let n be Element of NAT;
  assume n in dom c;
  then 1 <= n & n <= len c by FINSEQ_3:25;
  hence thesis by A1,Lm3;
end;
