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

theorem
  for S being ConstructorSignature
  for o being OperSymbol of S st o is constructor
  holds the_arity_of o = (len the_arity_of o) |-> a_Term
proof
  let S be ConstructorSignature;
  let o be OperSymbol of S such that
A1: o <> * and
A2: o <> non_op;
  reconsider t = a_Term as Element of {a_Term} by TARSKI:def 1;
A3: len ((len the_arity_of o)|->a_Term) = len the_arity_of o by CARD_1:def 7;
A4: the_arity_of o in {a_Term}* by A1,A2,Def9;
  (len the_arity_of o)|->t in {a_Term}* by FINSEQ_1:def 11;
  hence thesis by A3,A4,Th6;
end;
