let T be _Tree; for a, b being Vertex of T holds (T .pathBetween (a,b)) .vertices() = (T .pathBetween (b,a)) .vertices()
let a, b be Vertex of T; (T .pathBetween (a,b)) .vertices() = (T .pathBetween (b,a)) .vertices()
(T .pathBetween (a,b)) .reverse() = T .pathBetween (b,a)
by Th31;
hence
(T .pathBetween (a,b)) .vertices() = (T .pathBetween (b,a)) .vertices()
by GLIB_001:92; verum