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 Th24:
  for f being homogeneous PartFunc of D*, D, n
   st dom f = n-tuples_on D holds arity f = n
proof
  let f be homogeneous PartFunc of D*, D, n;
  consider x being object such that
A1: x in n-tuples_on D by XBOOLE_0:def 1;
  reconsider x as Element of n-tuples_on D by A1;
  assume
A2: dom f = n-tuples_on D;
  then
A3: for x be FinSequence st x in dom f holds len x = n by CARD_1:def 7;
  x in dom f by A2;
  hence thesis by A3,MARGREL1:def 25;
end;
