reserve n,m,k,k1,k2,i,j for Nat;
reserve x,y,z for object,X,Y,Z for set;
reserve A for Subset of X;
reserve B,A1,A2,A3 for SetSequence of X;
reserve Si for SigmaField of X;
reserve S,S1,S2,S3 for SetSequence of Si;

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;
