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 Th14:
  R_Segment(Upper_Arc C,W-min C,E-max C,p) =
  Segment(Upper_Arc C,W-min C,E-max C,p,E-max C)
proof
  Upper_Arc C is_an_arc_of W-min C,E-max C by JORDAN6:50;
  then L_Segment(Upper_Arc C,W-min C,E-max C,E-max C) = Upper_Arc C
  by JORDAN6:22;
  hence Segment(Upper_Arc C,W-min C,E-max C,p,E-max C) =
  R_Segment(Upper_Arc C,W-min C,E-max C,p) /\ Upper_Arc C by JORDAN6:def 5
    .= R_Segment(Upper_Arc C,W-min C,E-max C,p) by JORDAN6:20,XBOOLE_1:28;
end;
