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 Th31:
  D in Union FNDSC(V,A)
  proof
    ex S being FinSequence st S IsNDRankSeq V,A & D in Union S by Def5;
    hence thesis by Lm1;
  end;
