theorem Th30:
  p is_orientedpath_of v1,v2,V & V c= U implies p is_orientedpath_of v1,v2,U
proof
  assume that
A1: p is_orientedpath_of v1,v2,V and
A2: V c= U;
  vertices(p) \ {v2} c= V by A1;
  then
A3: vertices(p) \ {v2} c= U by A2;
  p is_orientedpath_of v1,v2 by A1;
  hence thesis by A3;
end;
