High Quality Content by WIKIPEDIA articles! In mathematical logic, generalization (also universal generalization, GEN) is an inference rule of predicate calculus. It states that if vdash P (x) has been derived, then vdash forall x , P (x) can be derived. The full generalization rule allows for hypotheses to the left of the turnstile, but with restrictions. Assume ? is a set of formulas, ? a formula, and Gamma vdash phi(y) has been derived. The generalization rule states that Gamma vdash forall x phi(x) can be derived if x is not mentioned in ? and x does not occur in ?.

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