When proving a theorem, it is first necessary to write the axioms, the hypotheses, and the conclusion. Deciding what axioms to choose in the first place is crucial to the success of a theorem prover, but that problem is peripheral to the presentation that follows. In general, there is no procedure for deciding what axioms are necessary or sufficient. In some problem domains, standard sets of axioms are known and used. For example, in group theory and in Euclidean geometry, many researchers use the axioms given in Sections 2.5 and 2.6, respectively.