reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem
  for C being strict Category holds C is U-petit iff CatToSet C is U-petit
  proof
    let C be strict Category;
    hereby
      assume C is U-petit;
      then consider c be strict Category such that
A1:   c is U-element and
A2:   C ~= c;
      CatToSet c is U-set by A1,Th88;
      hence CatToSet C is U-petit by Th90,A2;
    end;
    assume CatToSet C is U-petit;
    then consider c be CategorySet such that
A3: c is U-set and
A4: CatToSet C ~= c;
    SetToCat c is U-element & C ~= SetToCat c by A4,Th87,A3,Th89;
    hence C is U-petit;
  end;
