theorem Th9:
  for C being non empty compact Subset of TOP-REAL 2
  holds C is horizontal iff N-bound C <= S-bound C
proof
  let C be non empty compact Subset of TOP-REAL 2;
A1: N-bound C >= S-bound C by SPRECT_1:22;
  C is horizontal iff N-bound C = S-bound C by SPRECT_1:16;
  hence thesis by A1,XXREAL_0:1;
end;
