
theorem Th34:
  for T being _Tree for a, b being Vertex of T for t being
  _Subtree of T st a in the_Vertices_of t & b in the_Vertices_of t holds T
  .pathBetween(a,b).vertices() c= the_Vertices_of t
proof
  let T be _Tree, a, b be Vertex of T, t be _Subtree of T;
  assume a in the_Vertices_of t & b in the_Vertices_of t;
  then reconsider a9 = a, b9 = b as Vertex of t;
  set Tp = T.pathBetween(a,b), tp = t.pathBetween(a9,b9);
  Tp.vertices() = tp.vertices() by Th33,GLIB_001:76;
  hence thesis;
end;
