reserve x,y for set;
reserve s,r for Real;
reserve r1,r2 for Real;
reserve n for Nat;
reserve p,q,q1,q2 for Point of TOP-REAL 2;

theorem
  for P being Subset of TOP-REAL 2, p1,p2,q1,q2 being Point of TOP-REAL 2 st
  P is_an_arc_of p1,p2
  holds Segment(P,p1,p2,q1,q2)=Segment(P,p2,p1,q2,q1)
proof
  let P be Subset of TOP-REAL 2, p1,p2,q1,q2 be Point of TOP-REAL 2;
  assume
A1: P is_an_arc_of p1,p2;
  then L_Segment(P,p1,p2,q2)=R_Segment(P,p2,p1,q2) by Th28;
  hence thesis by A1,Th28,JORDAN5B:14;
end;
