Double negation?

Hello everybody,

I found the following sentence in Tae Kim's Guide to Learning Japanese:

加賀先生： そうね。大体、 「こんにちは」と言うと思いますよ。 ただし、書く時 は「こんにちわ」じゃなくて、 「こんにちは」と書かなくてはなりません。

The translation given is:

Kaga-sensei: Well, mostly, I think people say "konnichiwa". Only, when you write it, you must write "konnichiha" and not "konnichiwa".

I have trouble understanding the structure of the last phrase:

「こんにちは」と書かなくてはなりません。

I don't know how this translates to: you must write "Konnichiha".

My own analysis of the phrase is as follows:

「こんにちは」と "Konnichiha" quote
書かなくて not write
は topic particle
なりません must not

Is this a case of double negation? "You must NOT NOT write "konnichiha"?

Thanks

Yes, you are NOT permitted to NOT write "konnichiha".

In other words,
「こんにちは」と書かないといけません。
To NOT write "konnichiha" is NO good.

Think like math

(-) x (-) = +

(no) x (no) = Yes...

Look up here:
http://thejapanesepage.com/grammar/chapter_three/nakerebanarimasen