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Why is this new proof so much longer than the old one? Can't you just do?
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With my proof, it is clear that the "data" part of the definition does not depend on
classical.choice
. I don't know if your definition is computable.There was a problem hiding this comment.
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This is just the old proof with
classical
slapped on top, so the data part should be computable as well.There was a problem hiding this comment.
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Your definition is noncomputable. My definition still compiles if I remove type annotations from
coe
but I'm not sure how much this will affect readability.There was a problem hiding this comment.
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Here is a bit more straightforward of an algorithm data-wise, but it still depends on
classical.choice
-- the goal is equivalent tox = a ∨ ¬x = a
, and I wouldn't be surprised if LEM could be proved from this definition.@vihdzp The reason it's not computable when you put
classical
at the beginning is that the generated term is of the formlet I := foo in bar
wherefoo
is the noncomputable classical decidability instance.