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
  global_overlapping(V,A,D,D) = D
  proof
    per cases;
    suppose
A1:   not D in A;
      dom D c= dom D;
      hence thesis by A1,Th65;
    end;
    suppose
A2:   D in A;
      D is TypeSCNominativeData of V,A by Def6;
      hence thesis by A2,Def16;
    end;
  end;
