
theorem Th14:
  for n being Nat,p1,p2 being Point of TOP-REAL n, P,P1
being non empty Subset of TOP-REAL n st P is_an_arc_of p1,p2 & P1 is_an_arc_of
  p2,p1 & P1 c= P holds P1=P
proof
  let n be Nat,p1,p2 be Point of TOP-REAL n, P,P1 be non empty
  Subset of TOP-REAL n;
  assume that
A1: P is_an_arc_of p1,p2 and
A2: P1 is_an_arc_of p2,p1 and
A3: P1 c= P;
  P1 is_an_arc_of p1,p2 by A2,JORDAN5B:14;
  hence thesis by A1,A3,JORDAN6:46;
end;
