reserve p, q, x, y for Real,
  n for Nat;
reserve X for non empty TopSpace,
  a, b, c, d, e, f for Point of X,
  T for non empty pathwise_connected TopSpace,
  a1, b1, c1, d1, e1, f1 for Point of T;

theorem
  for A being Path of a1,b1, B being Path of b1,c1, C being Path of c1,
  d1, D being Path of d1,e1 holds A+(B+C)+D, A+B+(C+D) are_homotopic
proof
A1: c1,d1 are_connected & d1,e1 are_connected by BORSUK_2:def 3;
  a1,b1 are_connected & b1,c1 are_connected by BORSUK_2:def 3;
  hence thesis by A1,Th35;
end;
