reserve T for non empty TopSpace,
  a, b, c, d for Point of T;

theorem Th43:
  a,b are_connected implies for A being Path of a,b holds A = --A
proof
  set I = the carrier of I[01];
  assume
A1: a,b are_connected;
  let A be Path of a,b;
  for x being Element of I holds A.x = (--A).x
  proof
    let x be Element of I;
    reconsider z = 1-x as Point of I[01] by JORDAN5B:4;
    thus (--A).x = (-A).(1-x) by A1,BORSUK_2:def 6
      .= A.(1-z) by A1,BORSUK_2:def 6
      .= A.x;
  end;
  hence thesis by FUNCT_2:63;
end;
