Por Nicholas Pischke (TU Darmstadt).

I show how proofs involving set-valued maximally monotone operators on inner product spaces can be treated in suitable higher-order logical systems which admit proof-theoretic metatheorems that allows for the extraction of computational content. I outline how the basic theory of these operators can be formally developed, how extensionality of a set-valued operator is characterized by maximality and related concepts and what kind of metatheorems can be derived using those systems. Lastly, I discuss how extensions of these systems motivated by mathematical practice can be developed in this context and how they are necessary for a recent application of the metatheorems.

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