theorem Th4:
  vs is_oriented_vertex_seq_of c implies vs is_vertex_seq_of c
proof
  assume
A1: vs is_oriented_vertex_seq_of c;
  then
A2: len vs = len c + 1;
  for n st 1<=n & n<=len c holds c.n joins vs/.n, vs/.(n+1) by A1,Th1;
  hence thesis by A2,GRAPH_2:def 6;
end;
