We provide a simple proof of a curious inequality for the binary entropy function, an inequality that has been used in two different contexts. In the 1980's, Boppana used this entropy inequality to prove lower bounds on Boolean formulas. More recently, the inequality was used to achieve major progress on Frankl's union-closed sets conjecture. Our proof of the entropy inequality uses basic differential calculus.

翻译：我们简单地证明二进制酶功能存在令人好奇的不平等。 二进制酶功能是两种不同情况下使用的不平等。 20世纪80年代,Boppana利用这种通制不平等来证明布尔兰公式的下限。 最近,这种不平等被用来在Frankl的工会封闭套装猜想上取得重大进展。 我们的通制不平等证据使用了基本的差别计算法。