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
  for f being non empty homogeneous PartFunc of D*, D, n
   st dom f c= n-tuples_on D holds arity f = n
proof
  let f be non empty homogeneous PartFunc of D*, D, n;
  consider x being object such that
A1: x in dom f by XBOOLE_0:def 1;
  assume
A2: dom f c= n-tuples_on D;
  then
A3: for x being FinSequence st x in dom f holds n = len x by CARD_1:def 7;
  reconsider x as Element of n-tuples_on D by A2,A1;
  x in dom f by A1;
  hence thesis by A3,MARGREL1:def 25;
end;
