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
  v in V & not v.-->a1 in A & not v.-->a2 in A &
  a1 is TypeSCNominativeData of V,A & a2 is TypeSCNominativeData of V,A
  implies
  global_overlapping(V,A,v.-->a1,v.-->a2) = v.-->a2
  proof
    assume that
A1: v in V and
A2: not v.-->a1 in A & not v.-->a2 in A and
A3: a1 is TypeSCNominativeData of V,A &
    a2 is TypeSCNominativeData of V,A;
    naming(V,A,v,a1) = v.-->a1 & naming(V,A,v,a2) = v.-->a2 by A1,A3,Def13;
    hence thesis by A2,Th65;
  end;
