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 Th31:
  W-bound D1 < E-bound D1
proof
A1: W-bound D1 <> E-bound D1 by Th15;
  W-bound D1 <= E-bound D1 by Th21;
  hence thesis by A1,XXREAL_0:1;
end;
