reserve C, P for Simple_closed_curve,
  a, b, c, d, e for Point of TOP-REAL 2;

theorem
  LE W-min(P),E-max(P),P
proof
A1: E-max(P) <> W-min(P) by TOPREAL5:19;
  W-min(P) in Upper_Arc(P) & E-max(P) in Lower_Arc(P) by JORDAN7:1;
  hence thesis by A1,JORDAN6:def 10;
end;
