reserve C for Category,
  C1,C2 for Subcategory of C;

theorem Th16:
  for C being Categorial Category, c being Object of C holds cat c = c
proof
  let C be Categorial Category, c be Object of C;
  the carrier of C is categorial by Def6;
  then c is Category;
  hence thesis by Def7;
end;
