theorem
  P is being_S-P_arc implies ex f being Function of I[01], (TOP-REAL 2)|
  P st f is being_homeomorphism
proof
  assume P is being_S-P_arc;
  then consider p1,p2 such that
A1: P is_an_arc_of p1,p2 by Th28;
  ex f being Function of I[01], (TOP-REAL 2)|P st f is being_homeomorphism
  & f.0 = p1 & f.1 = p2 by A1;
  hence thesis;
end;
