reserve i,i1,i2,i9,i19,j,j1,j2,j9,j19,k,l,m,n for Nat;
reserve r,s,r9,s9 for Real;
reserve D for set,
  f for FinSequence of D,
  G for Matrix of D;
reserve G for Go-board,
  p for Point of TOP-REAL 2;

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;
