
theorem
  for n being Nat holds for x being Element of dyadic(n)
  holds (axis(x)-1)/(2|^n) < x & x < (axis(x)+1)/(2|^n)
proof
  let n be Nat;
  let x be Element of dyadic(n);
A1: 0 + axis(x) < 1 + axis(x) & 0 < 2|^n by NEWTON:83,XREAL_1:8;
  x = axis(x)/(2|^n) & -1 + axis(x) < 0 + axis(x) by Def5,XREAL_1:8;
  hence thesis by A1,XREAL_1:74;
end;
