Bótakrafan er samþykkt að því gefnu að fylgiskjalið komi.

Bótakrafan is a compound noun:

• bóta- = compensation / damages
• krafa = claim, demand
• -n = the suffixed definite article, so the

So bótakrafan means the compensation claim or the claim for damages.

As a whole in this sentence, it is the subject of er samþykkt.

In Icelandic, the definite article is usually attached to the noun as a suffix instead of being a separate word like English the.

So:

• bótakrafa = a compensation claim
• bótakrafan = the compensation claim

and

• fylgiskjal = an attachment / supporting document
• fylgiskjalið = the attachment / the supporting document

This is completely normal in Icelandic.

It is best understood as a past participle used predicatively with er.

So:

• er samþykkt = is approved

This works a lot like English is approved.

The participle samþykkt agrees with the subject. Since bótakrafan is feminine singular, samþykkt is in the matching form.

It is a fixed, fairly formal expression meaning:

• provided that
• on condition that
• assuming that

So the sentence means that the approval is conditional.

This phrase is common in formal, administrative, and legal language.

Because the whole expression is built in two parts:

• að því gefnu = literally something like given that
• the second að introduces the clause that follows

So:

• að því gefnu að fylgiskjalið komi = provided that the attachment arrives / is submitted

To an English speaker, the double að may look strange, but in Icelandic this is normal inside this fixed expression.

Because in the expression að því gefnu að, the word gefnu agrees with því, which is in the dative neuter singular.

So this phrase is not something you usually build from scratch as a beginner; it is best learned as a set expression:

• að því gefnu að = provided that

Still, grammatically, gefnu is the past participle of gefa in the form required by því.

Because komi is the present subjunctive of koma, and after expressions like að því gefnu að, Icelandic often uses the subjunctive to show something that is:

• conditional
• uncertain
• not yet an established fact

So:

• kemur = indicative, more like a plain statement
• komi = subjunctive, appropriate for provided that ...

This is one of the most important grammar points in the sentence.

Literally, yes, komi comes from koma = to come.

But with documents, attachments, applications, and similar things, Icelandic often uses koma in the sense of:

• arrive
• be received
• be submitted

So here fylgiskjalið komi is more naturally understood in English as:

• the attachment is received
• the supporting document is submitted
• the attachment arrives

rather than a very literal comes.

Fylgiskjalið is nominative singular neuter definite.

Why nominative? Because it is the subject of komi:

• fylgiskjalið komi = the attachment arrives / is submitted

So the document is the thing doing the arriving, grammatically speaking.

Literally, er samþykkt means is approved.

In formal or administrative language, though, a sentence like this often means something like:

• the claim is approved, provided that ...
• the claim stands approved on the condition that ...

So the approval is being stated, but with a condition attached. In practice, that often comes close to English will be approved provided that ..., even though Icelandic uses er.

Yes, very much so.

The formal tone comes especially from:

• bótakrafan
• samþykkt
• að því gefnu að

This sounds like administrative, legal, or bureaucratic Icelandic.

In less formal language, you might more often see a simpler conditional structure, such as one using ef for if, but að því gefnu að is a standard formal way to express provided that.

Sometimes yes, but the meaning and tone are not exactly the same.

• ef = if
• að því gefnu að = provided that / on condition that

So ef is simpler and more neutral, while að því gefnu að sounds more formal and more explicitly conditional.

That means að því gefnu að is the better choice in official writing when the idea is not just if, but only on this condition.