French translation: à la lecture de / avec l\'accord des parties
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This is a preposition found a lot in legal-type documents, even though it is less often used in modern EN.
However, this is not really a 'set expression' as such, hence as F-XF has pointed out, there is no one set translation in every case.
The important thing is that in the sort of usage in your examples, there is no real temporal element to it, as there almost always is in everyday English: "Upon rounding the corner, he saw the car on fire"
In your example, it is (seems to be, from snippets) more causal than temporal, so you original suggestion of 'après' wouldn't usually fit in these sort of contexts. Though in some cases, "d'après" might!
'Upon' can however have a temporal meaning when it conveys the sense of '(if/)when' — "Title to the property will be transferred upon signature of the contract"
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4 mins confidence: peer agreement (net): +2
à la lecture de / avec l'accord des parties
Explanation: ça dépend de la phrase.
No one size fits all
FX Fraipont Belgium Local time: 18:24 Native speaker of: French PRO pts in category: 972
5 mins confidence:
et étant donné que
Bruno Fonseca Local time: 17:24 Specializes in field Native speaker of: French, Portuguese