
theorem Th1:
  for n being Nat holds for x being Real st
  x in dyadic(n) holds 0 <= x & x <= 1
proof
  let n be Nat;
  let x be Real;
  assume x in dyadic(n);
  then consider i being Nat such that
A1: i <= 2|^n and
A2: x = i/(2|^n) by Def1;
  0/(2|^n) <= i/(2|^n) & i/(2|^n) <= (2|^n)/(2|^n) by A1,XREAL_1:72;
  hence thesis by A2,XCMPLX_1:60;
end;
