let n be Nat; ( n > 0 implies [\(log (2,(2 * n)))/] = [\(log (2,((2 * n) + 1)))/] )
set l22n = log (2,(2 * n));
set l22np1 = log (2,((2 * n) + 1));
assume A1:
n > 0
; [\(log (2,(2 * n)))/] = [\(log (2,((2 * n) + 1)))/]
then
( [\(log (2,((2 * n) + 1)))/] <> [\(log (2,(2 * n)))/] + 1 & [\(log (2,((2 * n) + 1)))/] <= [\(log (2,(2 * n)))/] + 1 )
by Th11, Th12;
then
[\(log (2,((2 * n) + 1)))/] < [\(log (2,(2 * n)))/] + 1
by XXREAL_0:1;
then A2:
[\(log (2,((2 * n) + 1)))/] <= ([\(log (2,(2 * n)))/] + 1) - 1
by INT_1:7;
log (2,(2 * n)) <= log (2,((2 * n) + 1))
by A1, Th10, NAT_1:11;
then
[\(log (2,(2 * n)))/] <= [\(log (2,((2 * n) + 1)))/]
by Th9;
hence
[\(log (2,(2 * n)))/] = [\(log (2,((2 * n) + 1)))/]
by A2, XXREAL_0:1; verum