127:, not hypothetical judgments, then we can formalize the Hilbert-style deduction system in such a way that its rules of inference contain only judgments of a rather simple form. The same cannot be done with the other two deductions systems: as context is changed in some of their rules of inferences, they cannot be formalized so that hypothetical judgments could be avoided—not even if we want to use them just for proving derivability of tautologies.
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of judgments, and their conclusion is a judgment as well (thus, hypotheses and conclusions of proofs are judgments). A characteristic feature of the variants of
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in mathematical logic can be exploited also in foundation of type theory as well.
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contain some context-changing rules. Thus, if we are interested only in the
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in an expression of the object language, or the provability of a
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is not changed in any of their rules of inference, while both
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