reserve C for Simple_closed_curve,
  p,q,p1 for Point of TOP-REAL 2,
  i,j,k,n for Nat,
  r,s for Real;

theorem Th5:
  q in Lower_Arc C & q <> W-min C implies LE E-max C, q, C
proof
  E-max C in Upper_Arc C by JORDAN7:1;
  hence thesis by JORDAN6:def 10;
end;
