"Laid down" is a phrasal verb that means to place something in a horizontal position or to establish rules or principles. There are many synonyms for this phrase, including "set down," "put down," "established," "dictated," "prescribed," "promulgated," "ordained," "enacted," "implemented," "installed," "arranged," and "positioned." Each of these words carries slightly different connotations, but they can all be used to describe the act of laying something down or establishing guidelines. By utilizing these synonyms, writers and speakers can add variety and depth to their language while still conveying the same meaning.