
theorem Th8:
  for n,i being Nat st 0 <= i & i < 2|^n holds (i*2+1)/
  (2|^(n+1)) in dyadic(n+1) \ dyadic(n)
proof
  let n,i be Nat;
  assume that
 0 <= i and
A1: i < 2|^n;
A2: 0 + 1 <= i + 1 by XREAL_1:6;
  consider s being Nat such that
A3: s = i + 1;
A4: s*2 - 1 = i*2 + (1 + 0) by A3;
  s <= 2|^n by A1,A3,NAT_1:13;
  hence thesis by A2,A4,Th7;
end;
