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Coq has tactics which allow the user to write proofs in a "procedural" way, and some tactics run some proof-searching algorithms behind the scenes -> this might become cumbersome in Agda, but we have agreed that we can leverage our vast Agda resources here
a "proof certificate" for a translation relation can be either the Coq/Agda script which is used to generate the response, or the Coq/Agda type which embeds the equivalence of the two ASTs; this type can then be checked by Coq/Agda; IMO, I'd say we ideally want the latter because this moves the trusted core to just the type-checker
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