(set up or found; "She set up a literacy program")
(set up or lay the groundwork for; "establish a new department")
(establish the validity of something, as by an example, explanation or experiment; "The experiment demonstrated the instability of the compound"; "The mathematician showed the validity of the conjecture")
(institute, enact, or establish; "make laws")
(bring about; "The trompe l'oeil-illusion establishes depth")
(place; "Her manager had set her up at the Ritz")
(build or establish something abstract; "build a reputation")
(use as a basis for; found on; "base a claim on some observation")