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 be Path of a1, b1, Q be Path of b1, c1, R be Path of c1, d1
  holds (P + Q) + R, P + (Q + R) are_homotopic
proof
  let P be Path of a1, b1, Q be Path of b1, c1, R be Path of c1, d1;
A1: c1,d1 are_connected by BORSUK_2:def 3;
  a1,b1 are_connected & b1,c1 are_connected by BORSUK_2:def 3;
  hence thesis by A1,Th73;
end;
