for用法的语法问题

for后面不可以直接加to do。
应该是sleeping is for working esaily,working is for sleeping at ease 。
意思是：睡觉是为了轻松的工作，工作是为了容易的入眠。
在这里for充当介词表示目的，介词后接名词如果接动词要改为动名词。而to do也表示目的。如果将这句用to do表示，如下：
sleeping is to work esaily,working is to sleep at ease 。

怎么这么别扭～～
sleeping is to work easily.
sleeping is for working easily.

后面那句同理。

sth is for to do - 这句不通

sth is for doing
sth is for sth

sth is to do 已经 表达了 意思， 不用 for