reserve r,lambda for Real,
  i,j,n for Nat;
reserve p,p1,p2,q1,q2 for Point of TOP-REAL 2,
  P, P1 for Subset of TOP-REAL 2;
reserve T for TopSpace;
reserve f,f1,f2,h for FinSequence of TOP-REAL 2;

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;
