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 Th20:
  for f being homogeneous NAT*-defined Function holds
  dom f c= (arity f)-tuples_on NAT
proof
  let f be homogeneous NAT*-defined Function;
  let x be object;
  assume
A1: x in dom f;
  reconsider x9 = x as FinSequence of NAT by A1,FINSEQ_1:def 11;
  len x9 = arity f by A1,MARGREL1:def 25;
  then x9 is Element of (arity f)-tuples_on NAT by FINSEQ_2:92;
  hence thesis;
end;
