theorem Th29:
  p is_orientedpath_of v1,v2,V & v1 <> v2 implies v1 in V
proof
  assume that
A1: p is_orientedpath_of v1,v2,V and
A2: v1 <> v2;
  p is_orientedpath_of v1,v2 by A1;
  then
A3: v1 in vertices p by Th27;
  not v1 in {v2} by A2,TARSKI:def 1;
  then
A4: v1 in vertices(p) \ {v2} by A3,XBOOLE_0:def 5;
  vertices(p) \ {v2} c= V by A1;
  hence thesis by A4;
end;
