Any person having an interest in any land within the district may file with the secretary a verified petition alleging all of the following:

1. (a) His land or a described portion of it was when it became a part of the district irrigated from another system of works than the works of or proposed for the district.
2. (b) It has continued ever since to be exclusively so irrigated.
3. (c) It is entitled to a special rate of assessment.