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 Th52:
  {v,v1} c= V & {a,a1} c= A implies
  ND_ex_3(v,v1,a,a1) is NonatomicND of V,A
  proof
    assume
A1: {v,v1} c= V & {a,a1} c= A;
    take <*NDSS(V,A)*>;
    thus <*NDSS(V,A)*> IsNDRankSeq V,A by Th27;
    ND_ex_3(v,v1,a,a1) in NDSS(V,A) by A1,Th51;
    hence thesis by FINSEQ_3:135;
  end;
