theorem
  AcyclicPaths(v1,v2) c= OrientedPaths(v1,v2)
proof
  let x be object;
  assume x in AcyclicPaths(v1,v2);
  then consider p being Simple oriented Chain of G such that
A1: x=p and
A2: p is_acyclicpath_of v1,v2;
  p is_orientedpath_of v1,v2 by A2;
  hence thesis by A1;
end;
