I'm trying to read this article (linked to in a different French.SE question). The very first sentence gives me difficulty!
L’autorité de Claude Muller en matière d’indéfinis n’est plus à démontrer.
deepL translates this to:
Claude Muller's authority on the subject of indefinites needs no further demonstration.
and if I click on "needs no futher" to get an alternative translation, DeepL gives a translation that is closer to my understanding of ne..plus :
Claude Muller's authority on the subject of indefinites no longer needs to be demonstrated.
I know that "à + infinitive" is called the "passive infinitive", and often follows a noun, for example "chambre à louer". It can be translated as "for ___ing", as in "room for renting". The answer to this question explains this in different words:
That form "à + infinitif" expresses the goal of potentially accomplishing the action.
Je te sers quelque chose à boire ?
Something to drink
With this information, I'm still not able to understand deepL's translation. "à démontrer" isn't being applied to a noun. The closest translation I can guess is "Claude's authority .. no longer is for demonstrating" or "... no longer is something to potentially demonstrate". I don't see how the idea of need can be found in "n'est plus à démontrer".
I thought that "être à + infinitive" might be an idiom, but looking through larousse's results after searching for "être à" doesn't seem to have an entry for "être à + infinitive".
(edit: actually, the page on Larousse does in fact have an entry for "être à", which (among other things) talks about obligation. I don't know why I didn't see it originally? However, the answers below are very helpful with their additional examples and their systematic elaboration about the "être à + infinitive" expressing obligation)
- How can I understand how "n'est plus à démontrer" can be translated to "needs no further demonstration"?
- Is there a way I can have looked this up myself, using the Internet (eg a dictionary, or some other resource)? Or, is there a way I could have guessed the meaning of "n'est plus à démonterer"?
- This grammar page on the passive infinitive has example sentences, but none of these sentences has the passive infinitive attached to a verb. Can you give me example sentences where "à + infinitive" is attached to a verb, as it is with "être à démontrer"?