moving from one place to another and back again; "he traveled back and forth between Los Angeles and New York"; "the treetops whipped to and fro in a frightening manner"; "the old man just sat on the porch and rocked back and forth all day"
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"
prove formally; demonstrate by a mathematical, formal proof
obtain probate of; "prove a will"
take a trial impression of
be shown or be found to be; "She proved to be right"; "The medicine turned out to save her life"; "She turned up HIV positive"