theorem Th19:
  for sc9 being Simple oriented Chain of G
  holds sc9 is oriented simple Chain of G
proof
  let sc9 be Simple oriented Chain of G;
  consider vs such that
A1: vs is_oriented_vertex_seq_of sc9 and
A2: for n,m st 1<=n & n<m & m<=len vs & vs.n=vs.m holds n=1 & m=len vs by Def7;
  vs is_vertex_seq_of sc9 by A1,Th4;
  hence thesis by A2,GRAPH_2:def 9;
end;
