S_1-Frankl 猜想的6元情形（I）

并封闭集猜测（又称Frankl猜测）说的是：对于任意由有限集合构成的一个有限集族，如果这个集族不仅仅包含空集的话，一定存在一个元素至少属于这个集族中一半的集合。在文献【3】中，作者提出了一个加强的Frankl猜测（简称S-Frankl猜测），并给出了部分证明。特别地，在【3】中作者证明了如果集族的元素个数n=5的话S-Frankl猜测成立。在此，我们拟证明n=6时也成立。由于整个论文太长，我们将论文分成两部分，这是第一部分。

The 6-element case of S_1-Frankl conjecture (I)

The union-closed sets conjecture (Frankl''s conjecture) says that for any nite union-closed family of nite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family. In 3], a stronger version of Frankl''s conjecture (S-Frankl conjecture for short) was introduced and a partial proof was given. In particular, it was proved in 3] that S-Frankl conjecture holds if n>=5, where n is the number of all the elements in the family of sets. Now, we want to prove that it holds if n = 6. Since the paper is very long, we split it into two parts. This is the first part.