Trouble with a sentence


I'm having trouble with the following line from Death note (anime):

> Light: これはお互いが、「深まった」と了承しあう為の儀式だ！

(context is that 2 characters are playing tennis to try to psychologically out
do the other)

The translation I have, reads:

> This is just a ritual to acknowledge that we've become friends.

I don't understand where the "just" comes from.

I had it more literally like this: "As for this, it is a mutual
acknowledgement ritual of our meeting to deepen our friendship". I don't
understand what the first part is doing in relation to the last part and why
we have し and 為 both indicating the reason for something. How the が fights in
is also puzzling.

If someone could dissect and explain the grammar operation here that would
help.




>   * これは儀式だ！ This is a ritual!
>   * これは[Vする]ための儀式だ！ This is a ritual to [verb]!
>   * これは[S]が[Vする]ための儀式だ！ This is a ritual for [S] to [verb]!
>   * これは[お互い]が、[「深まった」と了承しあう]ための儀式だ！  
>  This is a ritual for [both of us] to [mutually acknowledge that (our
> relationship) has been deepened]!
>

A simpler example would be これは子どもが読むための本です。 "This is a book for children to
read."

I would say the official translation is more literal, except for "just" which
came from nowhere. This "just" has been added by the translator to make the
sentence clearer.

お互い here is a noun that roughly means "both of us", which is naturally marked
with が and works as the subject of the verb 了承しあう.

For the difference between 了承する and 了承しあう, see: [Usage of 合える with verb
stems](https://japanese.stackexchange.com/q/28012/5010)

Lastly, Japanese commas play a smaller role on grammatical interpretation (see
[this question](https://japanese.stackexchange.com/a/23782/5010) for example).
Don't try to split this sentence into two by that comma.




>   * これは儀式だ！ This is a ritual!
>   * これは[Vする]ための儀式だ！ This is a ritual to [verb]!
>   * これは[S]が[Vする]ための儀式だ！ This is a ritual for [S] to [verb]!
>   * これは[お互い]が、[「深まった」と了承しあう]ための儀式だ！  
>  This is a ritual for [both of us] to [mutually acknowledge that (our
> relationship) has been deepened]!
>

A simpler example would be これは子どもが読むための本です。 "This is a book for children to
read."

I would say the official translation is more literal, except for "just" which
came from nowhere. This "just" has been added by the translator to make the
sentence clearer.

お互い here is a noun that roughly means "both of us", which is naturally marked
with が and works as the subject of the verb 了承しあう.

For the difference between 了承する and 了承しあう, see: [Usage of 合える with verb
stems](https://japanese.stackexchange.com/q/28012/5010)

Lastly, Japanese commas play a smaller role on grammatical interpretation (see
[this question](https://japanese.stackexchange.com/a/23782/5010) for example).
Don't try to split this sentence into two by that comma.

