After having done it (efter at have spist)

At have + participle

An infinitive can describe something that is already done. It is built like the perfect tense, but with the infinitive at have instead of har or havde:

perfectperfect infinitive
Jeg har spist.(efter) at have spist
Han har sagt farvel.(uden) at have sagt farvel

It follows the same words that take an ordinary infinitive — efter, uden, for and adjectives like glad for:

After having eaten, we went for a walk.
Efter at have spist gik vi en tur.
She left without having said goodbye.
Hun gik uden at have sagt farvel.
I am glad to have met you.
Jeg er glad for at have mødt dig.

When the phrase opens the sentence, the main clause starts with its verb, exactly as after any fronted adverbial:

After having read the book, I understood more.
Efter at have læst bogen forstod jeg mere.

Ikke

In a negative, ikke comes before at:

It was stupid not to have asked.
Det var dumt ikke at have spurgt.

Verbs that form their perfect with være use at være here: efter at være kommet hjem (after having come home).

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