theorem
  for A being horizontal Subset of TOP-REAL 2 holds A /\ B is horizontal
proof
  let A be horizontal Subset of TOP-REAL 2;
  let p, q be Point of T2;
  assume that
A1: p in A /\ B and
A2: q in A /\ B;
A3: p in A by A1,XBOOLE_0:def 4;
  q in A by A2,XBOOLE_0:def 4;
  hence thesis by A3,SPPOL_1:def 2;
end;
