theorem
  for A1,A2 being Path of a1,b1, B being Path of a1,c1 holds A1,A2
  are_homotopic implies A1, B+-B+A2 are_homotopic
proof
  a1,b1 are_connected & a1,c1 are_connected by BORSUK_2:def 3;
  hence thesis by Th25;
end;
