demonstrate vs bear witness

demonstrate and bear witness both are verbs.

Word	Noun	Adjective	Verb	Adverb
demonstrate	No	No	Yes	No
bear witness	No	No	Yes	No

As verbs, bear witness is a hypernym of demonstrate; that is, bear witness is a word with a broader meaning than demonstrate:

demonstrate: provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes
bear witness: provide evidence for

Other hypernyms of demonstrate include evidence, prove, show, testify.

demonstrate (verb)	bear witness (verb)
establish the validity of something, as by an example, explanation or experiment	give testimony in a court of law
provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes	provide evidence for
give an exhibition of to an interested audience
march in protest; take part in a demonstration