关于w.l.o.g. (without loss of generality)

"Without loss of generality assume that P" means that the restriction P placed on the objects being studied is not really a restriction - it just makes the proof less messy.

Often P is a restriction that some coefficient is 1 or 0, which makes expressions in the proof shorter and easier to read and understand.

Any similar object without that restriction is equivalent to the particular one, usually by some translation or scaling that doesn't affect the property being proved.

   从以上解释可以看出，应该理解为不失一般性的假设，并不特指在假设下成立，而是这种假设只是为了更好的说明问题。