theorem Th49:
  B is non-ascending implies superior_setsequence(B) = B
proof
  assume B is non-ascending;
  then (superior_setsequence(B)).n = B.n by Th48;
  then for n being Element of NAT holds (superior_setsequence(B)).n = B.n;
  hence thesis by FUNCT_2:63;
end;
