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 n,
  p1,p2 being Point of TOP-REAL n st P is_an_arc_of p1,p2 holds P\{p1,p2}<>{}
proof
  let P be Subset of TOP-REAL n, p1,p2 be Point of TOP-REAL n;
  assume P is_an_arc_of p1,p2;
  then consider p3 being Point of TOP-REAL n such that
A1: p3 in P and
A2: p3<>p1 and
A3: p3<>p2 by Th42;
  not p3 in {p1,p2} by A2,A3,TARSKI:def 2;
  hence thesis by A1,XBOOLE_0:def 5;
end;
