reserve C for Simple_closed_curve,
  A,A1,A2 for Subset of TOP-REAL 2,
  p,p1,p2,q ,q1,q2 for Point of TOP-REAL 2,
  n for Element of NAT;

theorem Th2:
  Segment(A,p1,p2,q1,q2) c= A
proof
  Segment(A,p1,p2,q1,q2) = R_Segment(A,p1,p2,q1) /\ L_Segment(A,p1,p2,q2)
  by JORDAN6:def 5;
  then
  R_Segment(A,p1,p2,q1) c= A & Segment(A,p1,p2,q1,q2) c= R_Segment(A,p1,p2
  ,q1) by JORDAN6:20,XBOOLE_1:17;
  hence thesis;
end;
