reserve a,b,c,v,v1,x,y for object;
reserve V,A for set;
reserve d for TypeSCNominativeData of V,A;

theorem Th14:
  for d1 being NonatomicND of V,A
    for d2 being TypeSCNominativeData of V,A
   st v in V & not d1 in A & not naming(V,A,v,d2) in A
  holds dom local_overlapping(V,A,d1,d2,v) = {v} \/ dom d1
  proof
    let d1 be NonatomicND of V,A;
    let d2 be TypeSCNominativeData of V,A such that
A1: v in V & not d1 in A & not naming(V,A,v,d2) in A;
    per cases;
    suppose
A2:   v in dom d1;
      then dom local_overlapping(V,A,d1,d2,v) = dom d1 by A1,Th13;
      hence thesis by A2,ZFMISC_1:40;
    end;
    suppose not v in dom d1;
      hence thesis by A1,Th12;
    end;
  end;
