I know that my math teacher can "prove" a theorem. For me to learn from her, though, must she "prove" an asset to me or "prove to be" an asset to me? In the first example, I know "theorem" is an object to the transitive verb "prove". In the 2nd and 3rd examples, what is "prove" and what is "asset"? A nice explanation from some knowledgeable grammarians with examples of other verbs that cause this confusion would be most instructive.