
theorem Th29:
  for T being _Tree, a, b being Vertex of T holds a in T
  .pathBetween(a,b).vertices() & b in T.pathBetween(a,b).vertices()
proof
  let T be _Tree, a, b be Vertex of T;
  T.pathBetween(a,b).first() = a by Th28;
  hence a in T.pathBetween(a,b).vertices() by GLIB_001:88;
  T.pathBetween(a,b).last() = b by Th28;
  hence thesis by GLIB_001:88;
end;
