Synonyms for Demonstrate (same or very similar meaning)
WordNet sense 1 (march in protest; take part in a demonstration):
march
WordNet sense 2 (show or demonstrate something to an interested audience):
demo, exhibit, present, show
WordNet sense 3 (provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes):
attest, certify, evidence, manifest
WordNet sense 4 (establish the validity of something, as by an example, explanation or experiment):
prove, shew, establish
From the ODE community, based on WordNet
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