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

theorem
  for d1,d2 being TypeSCNominativeData of V,A holds
   d2 c= global_overlapping(V,A,d1,d2)
  proof
    let d1,d2 be TypeSCNominativeData of V,A;
    per cases;
    suppose 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 NOMIN_1:def 16;
      hence thesis by XBOOLE_1:7;
    end;
    suppose d1 in A or d2 in A;
      hence thesis by NOMIN_1:def 16;
    end;
  end;
