
theorem
  for T being _Tree, a being Vertex of T holds T.pathBetween(a,a) = T.walkOf(a)
proof
  let T be _Tree, a be Vertex of T;
  consider b being Vertex of T such that
    A1: T.pathBetween(a,a) = T.walkOf(b) by GLIB_001:128;
  {a} = T.pathBetween(a,a).vertices() by HELLY:30
    .= {b} by A1, GLIB_001:90;
  hence thesis by A1, ZFMISC_1:3;
end;
