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nLab

weakening rule

# The weakening rule

## Idea

In logic, the *weakening rule* states that premises may be added to the hypotheses of a valid deduction while remaining valid. Along with the contraction rule and the exchange rule, it is one of the most commonly adopted structural rules.

The weakening rule is not used in all logical frameworks, for instance in linear logic it is discarded.

## Statements

Exactly how this looks depends on the logic used.

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