reserve fi,psi for Ordinal-Sequence,
  A,A1,B,C,D for Ordinal,
  X,Y for set,
  x,y for object;

theorem
  {} div^ A = {} & {} mod^ A = {} & A mod^ {} = A
proof
A1: A = {} or A <> {};
  {} = {}*^A by ORDINAL2:35;
  hence {} div^ A = {} by A1,Def6,Th68;
  thus {} mod^ A = {} by Th56;
  thus A mod^ {} = A-^{} by ORDINAL2:38
    .= A by Th56;
end;
