they had assumed
-avaient supposé
Past perfect they conjugation of assume.

assume

Within a few years they had assumed the work of forming the clergy.
Au bout de très peu d’années ils eurent à assumer le travail de formation du clergé.
Those Members that withheld payment undermined the commitment they had assumed in joining the United Nations and hobbled the Organization's effectiveness.
Les réticences manifestées par certains vont à l'encontre de l'engagement qu'ils ont pris à l'égard de l'Organisation et nuisent à son efficacité.
Belgium welcomed the existence of a protocol and expressed the hope that, despite its weaknesses, it would be a solid and useful instrument serving to remind those who used children on the battlefield of the obligations which they had assumed.
La Belgique se réjouissait de l'existence d'un protocole et a exprimé l'espoir que celui-ci, malgré ses faiblesses, puisse constituer un instrument utile et solide permettant de rappeler ceux qui se servaient d'enfants sur les champs de bataille aux obligations qu'ils avaient souscrites.
They had assumed that the authority of the congress was in violable, but had run into a stone wall of distrust and hostility.
Elles avaient compté sur une irrécusable autorité du Congrès, mais s'étaient heurtées à une muraille de défiance et d'hostilité. "
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