theorem Th132:
  for R being finite Subset of REAL holds R <> {} implies R is
bounded_above & upper_bound(R) in R & R is bounded_below & lower_bound(R) in R
proof
  let R be finite Subset of REAL;
  assume
A1: R <> {};
  P[card R] by Lm9;
  hence thesis by A1;
end;
