reserve i, j, k, c, m, n for Nat,
  a, x, y, z, X, Y for set,
  D, E for non empty set,
  R for Relation,
  f, g for Function,
  p, q for FinSequence;

theorem Th31:
  arity (n const m) = n
proof
  set d = the Element of n-tuples_on NAT;
A2: for x be FinSequence st x in dom (n const m) holds n=len x by CARD_1:def 7;
  d in dom (n const m);
  hence thesis by A2,MARGREL1:def 25;
end;
