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;

theorem Th32:
  S-bound D2 < N-bound D2
proof
A1: S-bound D2 <> N-bound D2 by Th16;
  S-bound D2 <= N-bound D2 by Th22;
  hence thesis by A1,XXREAL_0:1;
end;
