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 Th45:
  B is non-descending implies (inferior_setsequence B).n = B.n
proof
  assume B is non-descending;
  then (inferior_setsequence B).(n+1) /\ B.n = B.n by Th44,XBOOLE_1:28;
  hence thesis by Th21;
end;
