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I've just started reading Rijke's lecture notes on homotopy type theory. In the derivation of the element conversion rule posted here, the user infers $\Gamma \vdash A' \; \text{type}$ from $\Gamma \vdash A \doteq A' \; \text{type}$. The inference is obviously truth-preserving, but Rijke does not include it as a separate inference rule. Is there a way to circumvent this?

Viktor Glushkov
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    I cannot comment on the particular formal system you are looking at, but in general there is a notion of admissible rules of inference, which are rules that can be added to a formal system without changing what can be inferred. Admissibility is usually proved by proof analysis. – Zhen Lin Mar 15 '25 at 13:01

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