
theorem Th21:
  for eps being Real st 0 < eps
   ex n being Nat st 1 < 2|^n * eps
proof
  let eps be Real;
  assume
A1: 0 < eps;
  consider n being Nat such that
A2: 1 / eps < n by SEQ_4:3;
  take n;
  n < 2|^n by NEWTON:86;
  then 1/eps < 2|^n by A2,XXREAL_0:2;
  then 1/eps * eps < 2|^n * eps by A1,XREAL_1:68;
  hence thesis by A1,XCMPLX_1:87;
end;
