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  • $\begingroup$ Thank you! So in Agda, the contextual information (say, which terms are equivalent) doesn't hold across functions. Is that correct? $\endgroup$ Commented Oct 13, 2018 at 20:18
  • $\begingroup$ I'm not sure what you mean. Can you give an example? $\endgroup$ Commented Oct 13, 2018 at 21:21
  • $\begingroup$ Like, if a parameter of type $a \equiv b$ is matched as $refl$, $a$ and $b$ will be treated as equivalent in the context. We have to bring this information out of the generated helper function (by introducing an explicit argument whose value is trivially $a$) so that we can make use of it in the proofs. $\endgroup$ Commented Oct 13, 2018 at 23:48
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    $\begingroup$ From the outside, we only learn about the behaviour of wa''-aux when the proof we pass to it is judgmentally refl, matching the definition clause. comm n m is not judgmentally refl – it is an inductive argument. Whenever we do pass in refl, we've already done the same unification on the outside as has been done on the inside, so generally, this unification information doesn't leak. $\endgroup$ Commented Oct 14, 2018 at 0:03