establish vs lay down

establish and lay down both are verbs.

Word	Noun	Adjective	Verb	Adverb
establish	No	No	Yes	No
lay down	No	No	Yes	No

As verbs, establish and lay down are synonyms defined as:

Other synonyms of establish include make.

establish (verb)	lay down (verb)
establish the validity of something, as by an example, explanation or experiment	institute, enact, or establish
institute, enact, or establish
use as a basis for; found on
place
set up or lay the groundwork for
bring about
build or establish something abstract
set up or found