on the assumption that

used to introduce a condition that is considered as the basis for a particular action or decision

We proceeded with the project on the assumption that the funding would be approved.
They made plans for the event on the assumption that the weather would cooperate.
The company implemented cost-cutting measures on the assumption that there would be a downturn in the economy.
She accepted the job offer on the assumption that there would be opportunities for advancement.
He invested in the stock market on the assumption that the company's profits would continue to grow.