Laid it down is a common phrase that can be used in many different contexts. However, to add variation and depth to your writing or speaking, it is useful to know various synonyms for the phrase. Some common alternatives for laid it down include "set," "put forth," "established," "declared," "asserted," "articulated," "promulgated," "proposed," "stated," "presented," "proffered," and "affirmed." Each of these words conveys a slightly different meaning and can be tailored to the specific situation at hand. By using a variety of synonyms, you can prevent your speech or writing from sounding repetitive and dull.