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,Th33;
end;
