reserve i, j, m, n for Nat,
  z, B0 for set,
  f, x0 for real-valued FinSequence;

theorem Th31:
  for n being non zero Nat holds RN_Base n <> {}
proof
  let n be non zero Nat;
  0+1 <= n by NAT_1:13;
  then
  Base_FinSeq(n,1) in { Base_FinSeq(n,i) where i is Element of NAT: 1<=i &
  i<=n};
  hence thesis;
end;
