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Symbolic Deduction in Mathematical Databases based on Properties

We claim that mathematical databases should be more than a collection of domains with associated theorems; in particular theorems should be stated as general as possible, that is independent of domains. A database then should be able to check whether such a general theorem holds in a particular domain. To this end we use a properties-based representation for both theorems and domains, and present a deduction calculus that using additional rules about the problem domain allows to perform such a theorem check.