Structural rule A famous structural rule is known as cut. Considerable effort is spent by proof theorists in showing that cut rules are superfluous in various logics. More precisely, what is shown is that cut is only (in a sense) a tool for abbreviating proofs, and does not add to the theorems that can be proved. The successful 'removal' of cut rules, known as "cut elimination", is directly related to the philosophy of "computation as normalization" (see Curry–Howard correspondence); it often gives a good indication of the complexity of deciding a given logic. Structural rule In proof theory, a structural rule is
Zaitsev's rule the University of Kazan in 1873. Zaitsev had cited Popov's 1872 paper in previous work and worked at the University of Kazan, and was thus probably aware of Popov's proposed rule. In spite of this, Zaitsev's 1875 "Liebigs Annalen" paper makes no mention of Popov's work. Any discussion of Zaitsev's rule would be incomplete without mentioning Vladimir Vasilyevich Markovnikov. Zaitsev and Markovnikov both studied under Alexander Butlerov, taught at the University of Kazan during the same period, and were bitter rivals. Markovnikov, who published in 1870 what is now known as Markovnikov's rule, and Zaitsev held conflicting views regarding elimination