theorem Th3: :: ENTROPY1:3

for r being Real st r > 0 holds
( log (number_e,r) <= r - 1 & ( r = 1 implies log (number_e,r) = r - 1 ) & ( log (number_e,r) = r - 1 implies r = 1 ) & ( r <> 1 implies log (number_e,r) < r - 1 ) & ( log (number_e,r) < r - 1 implies r <> 1 ) )