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 Th65:
  not D1 in A & not D2 in A & dom D1 c= dom D2 implies
  global_overlapping(V,A,D1,D2) = D2
  proof
    assume
A1: not D1 in A & not D2 in A;
    assume
A2: dom D1 c= dom D2;
    thus global_overlapping(V,A,D1,D2) = D2 \/ (D1|(dom(D1)\dom(D2)))
    by A1,Th64
    .= D2 \/ (D1|{}) by A2,XBOOLE_1:37
    .= D2;
  end;
