Forutsatt at slettingen etter feilsendingen er bekreftet, avslutter vi saken.

Forutsatt at means something like provided that, assuming that, or on the condition that. It introduces a condition.

It is more formal than simple hvis or dersom.

Examples:

• Forutsatt at alt går som planlagt, møtes vi i morgen.
• Forutsatt at betalingen er registrert, sender vi varen.

So in your sentence, forutsatt at sets up the condition that must be true before the main action happens.

Forutsatt is originally the past participle of forutsette (to assume / presuppose / require), but in expressions like forutsatt at, it works almost like a fixed linking word.

So although it looks like a participle, learners often do best by treating forutsatt at as a set phrase meaning provided that.

You will often see:

• Forutsatt at ...
• Under forutsetning av at ...
  Both are formal ways to express a condition.

In Norwegian, the definite form is very common when talking about a specific thing already known from the situation or context.

Here:

• slettingen = the deletion
• feilsendingen = the mistaken sending / the incorrect transmission
• saken = the case / the matter

The sentence is referring to specific, identifiable things:

• a particular deletion
• a particular mistaken sending
• a particular case

That is why the definite endings are used:

• -en for masculine nouns like sletting, feilsending, sak

Here etter means after.

So etter feilsendingen means after the mistaken sending or following the erroneous transmission/sending.

This phrase tells you which deletion is being talked about: the deletion that happened after the error.

Structurally:

• etter = after
• feilsendingen = the mistaken sending

The noun feilsending is a compound:

• feil = error, wrong
• sending = sending, transmission

So feilsending is literally something like wrong-sending.

Yes, this is a very common Norwegian structure.

er bekreftet literally means is confirmed. It can be understood as:

• a passive-like construction, or
• a result state: the confirmation has already happened, and now it stands confirmed

Compare:

• Slettingen er bekreftet. = The deletion is confirmed.
• Slettingen ble bekreftet. = The deletion was confirmed.
  This focuses more on the event in the past.
• Slettingen har blitt bekreftet. = The deletion has been confirmed.
  This is also possible, but often heavier in style.

In formal written Norwegian, er + past participle is very common.

This is because Norwegian follows the V2 rule in main clauses: the finite verb must come in the second position.

The sentence begins with the conditional clause:

• Forutsatt at slettingen etter feilsendingen er bekreftet

That whole clause counts as the first element. So the finite verb in the main clause must come next:

• avslutter

Then the subject comes after the verb:

• vi

So:

• Forutsatt at ..., avslutter vi saken.

If there were no opening clause, you would say:

• Vi avslutter saken.

Yes, in normal writing a comma is used after an introductory subordinate clause like this.

So:

• Forutsatt at slettingen etter feilsendingen er bekreftet, avslutter vi saken.

The comma marks the end of the condition clause and the start of the main clause.

This is standard and especially common in formal written Norwegian.

Often yes, but the tone changes.

• Hvis slettingen etter feilsendingen er bekreftet, avslutter vi saken.
• Forutsatt at slettingen etter feilsendingen er bekreftet, avslutter vi saken.

Both are understandable, but:

• hvis = more neutral, everyday if
• forutsatt at = more formal, administrative, conditional, almost legalistic

In business or official communication, forutsatt at sounds very natural.

Yes, roughly. Å avslutte en sak means to close a case, bring a matter to an end, or close the issue.

In administrative, customer-service, or legal-style contexts, sak often means:

• case
• matter
• issue
• ticket/request, depending on context

So avslutter vi saken is a standard formal expression meaning that they will consider the matter closed.

Because at already introduces the subordinate clause, and Norwegian does not need anything else there.

The structure is simply:

• Forutsatt at
  • clause

That clause is:

• slettingen etter feilsendingen er bekreftet

In other words:

• subject: slettingen etter feilsendingen
• verb phrase: er bekreftet

No extra word like that is or which is is needed.

Yes. Norwegian often builds precise formal noun phrases by putting a noun in the definite form and then adding a prepositional phrase after it.

Here:

• slettingen = the deletion
• etter feilsendingen = after the mistaken sending

Together:

• slettingen etter feilsendingen = the deletion after the mistaken sending

This is very typical of formal or administrative Norwegian. English often prefers something a bit more expanded, but Norwegian can pack this information into one compact noun phrase.