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cut rule
In mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. Its meaning is that, if a formula ''A'' appears as a conclusion in one proof and an hypothesis in another, then another proof in which the formula ''A'' does not appear can be deduced. In the particular case of the modus ponens, for example occurrences of ''man'' are eliminated of ''Every man is mortal, Socrates is a man'' to deduce ''Socrates is mortal''.
== Formal notation ==
Formal notation in sequent calculus notation :
;cut:
:
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