reserve a,a1,a2,v,v1,v2,x for object;
reserve V,A for set;
reserve m,n for Nat;
reserve S,S1,S2 for FinSequence;
reserve D,D1,D2 for NonatomicND of V,A;

theorem Th42:
  not D in A implies D in ND(V,A) \ A
  proof
    D in ND(V,A) by Th41;
    hence thesis by XBOOLE_0:def 5;
  end;
