on the understanding that

/ɒnðɪ ˌʌndəstˈandɪŋ ðˈat/

/ɑːnðɪ ˌʌndɚstˈændɪŋ ðˈæt/

[phrase]

[PHRASE]

used when an agreement can only be reached under a specific condition

Examples

1. He took his family with him, the no-travel laws for Jews briefly waived on the understanding that the award would bring glory on Italy.

2. After nearly seven years, he’d agreed to write the fifth Hitchhiker’s book, on the understanding that it would be the last.

3. Seriously, he even brought a loyal group of school friends along with him, all of whom donned uniform for the first time on the understanding that they’d soon be overthrowing the government.

4. That is, the supporters of the ERA in the House and in the Senate, it was really Republican women like Margaret Heckler and Florence Dwyer who really stood up in favor of the ERA on the understanding that it would actually help women overcome disadvantages that they faced because they were mothers.