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 Th43:
  x in ND(V,A) \ A implies x is NonatomicND of V,A
  proof
    assume
A1: x in ND(V,A) \ A;
    then x in ND(V,A);
    then
A2: ex w being TypeSCNominativeData of V,A st x = w;
    not x in A by A1,XBOOLE_0:def 5;
    hence thesis by A2,Def6;
  end;
