reserve S, T, Y for non empty TopSpace,
  s, s1, s2, s3 for Point of S,
  t, t1, t2, t3 for Point of T,
  l1, l2 for Path of [s1,t1],[s2,t2],
  H for Homotopy of l1 ,l2;

theorem
  for S, T being non empty pathwise_connected TopSpace, s1, s2, s3 being
  Point of S, t1, t2, t3 being Point of T, l1 being Path of [s1,t1],[s2,t2], l2
  being Path of [s2,t2],[s3,t3] holds pr2 (l1+l2) = (pr2 l1) + (pr2 l2)
proof
  let S, T be non empty pathwise_connected TopSpace, s1, s2, s3 be Point of S,
t1, t2, t3 be Point of T, l1 be Path of [s1,t1],[s2,t2], l2 be Path of [s2,t2],
  [s3,t3];
  [s1,t1],[s2,t2] are_connected & [s2,t2],[s3,t3] are_connected by
BORSUK_2:def 3;
  hence thesis by Th25;
end;
