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 Th18:  :: poprawic JORDAN7:7
  C = Segment(W-min C,W-min C,C)
proof
  set X = {p: LE W-min C,p,C or W-min C in C & p=W-min C};
A1: Segment(W-min C,W-min C,C) = X by JORDAN7:def 1;
  thus C c= Segment(W-min C,W-min C,C)
  proof
    let e be object;
    assume
A2: e in C;
    then reconsider p = e as Point of TOP-REAL 2;
    LE W-min C,p,C by A2,JORDAN7:3;
    hence thesis by A1;
  end;
  thus thesis by JORDAN16:6;
end;
