reserve v for object;
reserve V,A for set;
reserve f for SCBinominativeFunction of V,A;

theorem Th4:
  A is_without_nonatomicND_wrt V & v in V implies
  for d1 being NonatomicND of V,A
    for d2 being TypeSCNominativeData of V,A
  holds dom local_overlapping(V,A,d1,d2,v) = {v} \/ dom d1
  proof
    assume that
A1: A is_without_nonatomicND_wrt V and
A2: v in V;
    let d1 be NonatomicND of V,A;
    let d2 be TypeSCNominativeData of V,A;
    not d1 in A & not naming(V,A,v,d2) in A by A1,Th3;
    hence thesis by A2,NOMIN_2:15;
  end;
