
theorem Th2:
  for X being non empty set, x being Element of X
  for n being Nat holds arity ((n-tuples_on X) --> x) = n
proof
  let X be non empty set;
  let x be Element of X;
  let n be Nat;
  reconsider m = n as Element of NAT by ORDINAL1:def 12;
  set f = (n-tuples_on X) --> x;
  dom f = m-tuples_on X by FUNCOP_1:13;
  hence thesis by COMPUT_1:24;
end;
