
theorem Th13:
  for n being Nat st n > 0 holds [\ log(2, 2*n) /] = [\ log(2, 2*n + 1) /]
proof
  let n be Nat;
  set l22n = log (2, 2*n);
  set l22np1 = log (2, 2*n + 1);
  assume
A1: n > 0;
  then [\l22np1/] <> [\l22n/] + 1 & [\l22np1/] <= [\l22n/] + 1 by Th11,Th12;
  then [\l22np1/] < [\l22n/] + 1 by XXREAL_0:1;
  then
A2: [\l22np1/] <= [\l22n/]+1-1 by INT_1:7;
  l22n <= l22np1 by A1,Th10,NAT_1:11;
  then [\l22n/] <= [\l22np1/] by Th9;
  hence thesis by A2,XXREAL_0:1;
end;
