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 Th64:
  not D1 in A & not D2 in A implies
  global_overlapping(V,A,D1,D2) = D2 \/ (D1|(dom(D1)\dom(D2)))
  proof
A1: D1 is TypeSCNominativeData of V,A by Def6;
A2: D2 is TypeSCNominativeData of V,A by Def6;
    assume not D1 in A & not D2 in A;
    then ex f1,f2 being Function st f1 = D1 & f2 = D2 &
    global_overlapping(V,A,D1,D2) = f2 \/ (f1|(dom(f1)\dom(f2)))
    by A1,A2,Def16;
    hence thesis;
  end;
