All property within the city, not exempt under the laws of the United States or the state of California, except property used exclusively for public schools, free public libraries, free museums and such as may belong to the United States, the State of California, the county of Tulare, or the city, and except such property as is subject to taxation pursuant to provisions of the Constitution and which taxes are declared by the Constitution to be in lieu of all other taxes, is subject to taxation as in this chapter provided, but nothing in this chapter shall be construed to require or permit double taxation. (Prior code § 1559)