prove oneself vs establish

prove oneself and establish both are verbs.

Word	Noun	Adjective	Verb	Adverb
prove oneself	No	No	Yes	No
establish	No	No	Yes	No

As verbs, establish is a hypernym of prove oneself; that is, establish is a word with a broader meaning than prove oneself:

prove oneself: show one's ability or courage
establish: establish the validity of something, as by an example, explanation or experiment

Other hypernyms of prove oneself include demonstrate, prove, shew, show.

prove oneself (verb)	establish (verb)
show one's ability or courage	establish the validity of something, as by an example, explanation or experiment
	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