
theorem Th31:
  for T being _Tree, a, b being Vertex of T holds T.pathBetween(a,
  b).reverse() = T.pathBetween(b,a)
proof
  let T be _Tree, a, b be Vertex of T;
  set P = T.pathBetween(a,b);
  P is_Walk_from a, b by Def2;
  then P.reverse() is_Walk_from b, a by GLIB_001:23;
  hence thesis by Def2;
end;
