reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem
  for C being ConstructorSignature holds the_arity_of non_op C = <*an_Adj C*> &
  the_result_sort_of non_op C = an_Adj C &
  the_arity_of ast C = <*an_Adj C, a_Type C*> &
  the_result_sort_of ast C = a_Type C by Def9;
