prove, demonstrate, establish, show, shew -- (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")
lay down, establish, make -- (institute, enact, or establish; "make laws")
establish, give -- (bring about; "The trompe l'oeil-illusion establishes depth")
install, instal, set up, establish -- (place; "Her manager had set her up at the Ritz")
build, establish -- (build or establish something abstract; "build a reputation")
establish, base, ground, found -- (use as a basis for; found on; "base a claim on some observation")