reserve n for Nat;

theorem Th23:
  for X,Y be non empty compact Subset of TOP-REAL 2 st N-bound X
  <= N-bound Y holds N-bound (X\/Y) = N-bound Y
proof
  let X,Y be non empty compact Subset of TOP-REAL 2;
  assume N-bound X <= N-bound Y;
  then max(N-bound X,N-bound Y) = N-bound Y by XXREAL_0:def 10;
  hence thesis by SPRECT_1:49;
end;
