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
  for D being TypeSCNominativeData of V,A holds D in Union FNDSC(V,A)
  proof
    let D be TypeSCNominativeData of V,A;
A1: D in A or D is NonatomicND of V,A by Def6;
    A c= Union FNDSC(V,A) by Th11;
    hence thesis by A1,Th31;
  end;
