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

theorem Th9:
  for d1,d2 being NonatomicND of V,A holds
   global_overlapping(V,A,d1,d2) is NonatomicND of V,A
  proof
    let d1,d2 be NonatomicND of V,A;
    per cases;
    suppose not d1 in A & not d2 in A;
      then
A1:   global_overlapping(V,A,d1,d2) = d2 \/ (d1|(dom(d1)\dom(d2)))
      by NOMIN_1:64;
      d1|(dom(d1)\dom(d2)) is NonatomicND of V,A by NOMIN_1:32,RELAT_1:59;
      hence thesis by A1,NOMIN_1:36,PARTFUN1:51;
    end;
    suppose d1 in A or d2 in A;
      hence thesis by NOMIN_1:def 16;
    end;
  end;
