reserve T for non empty TopSpace,
  a, b, c, d for Point of T;
reserve X for non empty pathwise_connected TopSpace,
  a1, b1, c1, d1 for Point of X;

theorem
  for P, Q being Path of a1, b1 st P, Q are_homotopic holds -P, -Q
  are_homotopic by Th77,BORSUK_2:def 3;
