
theorem Th30:
  for T being _Tree, a being Vertex of T holds T.pathBetween(a,a)
  .vertices() = {a}
proof
  let T be _Tree, a be Vertex of T;
  set P = T.pathBetween(a,a);
  consider v being Vertex of T such that
A1: P = T.walkOf(v) by GLIB_001:128;
  a = P.first() & T.walkOf(v).first() = v by Th28;
  hence thesis by A1,GLIB_001:90;
end;
