reserve S for Subset of TOP-REAL 2,
  C,C1,C2 for non empty compact Subset of TOP-REAL 2,
  p,q for Point of TOP-REAL 2;
reserve i,j,k for Nat,
  t,r1,r2,s1,s2 for Real;
reserve D1 for non vertical non empty compact Subset of TOP-REAL 2,
  D2 for non horizontal non empty compact Subset of TOP-REAL 2,
  D for non vertical non horizontal non empty compact Subset of TOP-REAL 2;
reserve s for rectangular FinSequence of TOP-REAL 2;

theorem Th87:
  r1 < r2 & s1 < s2 implies [.r1,r2,s1,s2.] is Jordan
proof
  assume that
A1: r1 < r2 and
A2: s1 < s2;
  [.r1,r2,s1,s2.] = { p: p`1 = r1 & p`2 <= s2 & p`2 >= s1 or p`1 <= r2 & p
`1 >= r1 & p`2 = s2 or p`1 <= r2 & p`1 >= r1 & p`2 = s1 or p`1 = r2 & p`2 <= s2
  & p`2 >= s1} by A1,A2,SPPOL_2:54;
  hence thesis by A1,A2,JORDAN1:43;
end;
