
theorem Th5:
  for n being Nat holds dyadic(n) c= dyadic(n+1)
proof
  let n be Nat;
  let x be object;
  assume
A1: x in dyadic(n);
  ex i being Nat st i <= 2|^(n+1) & x = i/(2|^(n+1))
  proof
    reconsider x as Real by A1;
    consider i being Nat such that
A2: i <= 2|^n & x = i/(2|^n) by A1,Def1;
    take i*2;
    2|^(n+1) = (2|^n)*2 by NEWTON:6;
    hence thesis by A2,XCMPLX_1:91,XREAL_1:64;
  end;
  hence thesis by Def1;
end;
