Examples of use of on the assumption
1. "We‘re working on the assumption that he‘s alive," she said.
2. It is based on the assumption that there are only two options: peace or war.
3. Until they can determine otherwise, police are operating on the assumption that she has been kidnapped.
4. "We started ColorOfChange on the assumption that we could do civil–rights–type work," he said.
5. Nine people detained without charge on the assumption they will be deported last Thursday are Algerian.