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 being
  Point of TOP-REAL 2 st P is_an_arc_of p1,p2 holds R_Segment(P,p1,p2,p1)=P
proof
  let P be Subset of TOP-REAL 2, p1,p2 be Point of TOP-REAL 2;
  assume
A1: P is_an_arc_of p1,p2;
  thus R_Segment(P,p1,p2,p1) c= P by Th20;
  let x be object;
  assume
A2: x in P;
  then reconsider p=x as Point of TOP-REAL 2;
  LE p1,p,P,p1,p2 by A1,A2,JORDAN5C:10;
  hence thesis;
end;
