reserve p,p1,p2,p3,q for Point of TOP-REAL 2;

theorem Th2:
  for P being compact non empty Subset of TOP-REAL 2,q st P is
  being_simple_closed_curve & LE q,W-min(P),P holds q=W-min(P)
proof
  let P be compact non empty Subset of TOP-REAL 2,q;
  assume P is being_simple_closed_curve & LE q,W-min(P),P;
  then
  LE q,W-min(P),Upper_Arc(P),W-min(P),E-max(P) & Upper_Arc(P) is_an_arc_of
  W-min(P),E-max(P) by JORDAN6:def 8,def 10;
  hence thesis by JORDAN6:54;
end;
